There are two elements I see here:

1. Did the ruling class in the colonies and early USA purposefully use racism and classism as tools to control the populace and maintain power. (I believe so.)

2. Does that mean that racism and classism are a conspiracy foisted upon the masses of the people to keep them in line. (Not in a real, conspiratorial sense. But it's complicated.)

This really gets to the heart of a sociological question, which manifests in history.

Racism and classism are examples of "social constructs" - frameworks of thought built by and into societies. An analysis of what social constructs are is way outside the scope of this answer, but the basic concept is that social constructs become a part of a people's social and cultural reality and influence the way people interact in society. But does that mean that a social construct is just something that happens? Was racism just in the air, so people started enslaving African peoples? Not really.

There are always people who are going to leverage social concepts as a tactic, and are there are always people who are developing new ideas and rhetoric which can make it into the cultural consciousness and become part of that social reality, but I think it's a huge mistake to look at something like racism and say "this is a conspiracy, cynically perpetuated by the powerful to keep the disempowered down", not because elements of that behavior don't ever happen, but because it misunderstands the psychological and sociological nature of social construction.

I think we can illustrate this a bit better by diving into the documented history of race and racism as a concept, but I want to start by putting a thought in your head, articulated by Max Weber (one of the 'founders' of what we today think of as sociology):

The fortunate man is seldom satisfied with the fact of being fortunate, beyond this he needs to know that he has a right to his good fortune. He wants to be convinced he deserves it and above all that he deserves it in comparison with others. Good fortune, thus wants to be legitimate fortune.

When we talk about individual people as actors, creating racism or classism, keep this idea in mind. Identity matters to people. Legitimacy matters to people.

Let's consider in brief, then, where 'racism' comes from. In Stamped from the Beginning: The Definitive History of Racist Ideas in America*,* Ibram Kendi points to a 1453 biography of Prince Henry the Navigator, commissioned by the King of Portugal (the nephew of Prince Henry). Henry was a slaver. He sailed to sub-Saharan Africa, and enslaved a whole bunch of different people. Now, a century prior, people were aware of the west African kingdoms, and were talking and writing about these diverse peoples as distinct, but when this biographer, commissioned by the king specifically to glorify his subject, is writing about those voyages, he lumps all those people together. He creates a grouping of sub-Saharan African peoples and says that they all lived "like beasts", and that by enslaving them and bringing them to Christian lands, Prince Henry was actually their benefactor.

This is the seed of an idea - rhetoric is created which didn't exist before, and deployed to justify and elevate the actions of the powerful. The enslaving already happened, and it happened for economic reasons - the justification comes after, in order to recast the narrative. But now that the idea exists in society, other people will start to latch onto it because it gives them a framework for justifying their behavior and ideology too. As the idea propagates it becomes normalized, and it becomes part of the lived socio-cultural 'reality' of these people.

So throughout the early modern period, European thinkers, businessmen, and leaders would take this idea, and refine or repurpose it within their own cultural contexts. This brings us to Zinn, and the history of race and policy in the colonies and early USA, which is where it gets a bit muddier to me.

We know that racialized thinking was present in the cultural consciousness of British colonists in the 1600s and 1700s, because they wrote and talked about it. We know that at the start of the colonial project, there wasn't a legal distinction between unfree labor done by people we would today call black and white, but at the time were identified more by religion and national origin. We know that in the middle of the 1600s legal actors began a project of integrating race into the legal code, which had the effect of alienating poor (and unfree) white people from poor (and unfree) black people. I've read or am aware of quite a few analyses of the period which assert (like Zinn does) that this was a deliberate political project by the elite class to break up a potential working class coalition of peoples who had a shared struggle, so that they could construct a cross-class coalition of white folks in support of the current social order.

Generally, I've seen it stated that interracial working class uprisings within the 1600s culminated with Bacon's Rebellion in 1676, and that this scared the Virginia House of Burgesses and was an explicit motivation for the Virginia Slave Acts of 1705. I know that in the latter half of the 1700s and through the 1800s, leading Americans wrote about limiting and controlling working class access to power, and I have seen several quotes by historic American politicians which contrast race and class divisions. The one that I see most often is Calhoun's comments on labor in the North vs. the South

There is no part of the world were agricultural, mechanical, and other descriptions of labor are more respected than in the South, with the exception of two descriptions of employment—that of menial and body servants. No Southern man—not the poorest or the lowest—will, under any circumstance, submit to perform either of them. He has too much pride for that, and I rejoice that he has. They are unsuited to the spirit of a freeman. But the man who would spurn them feels not the least degradation to work in the same field with his slave; or to be employed to work with them in the same field or in any mechanical operation; and, when so employed, they claim the right,—and are admitted, in the country portion of the South—of sitting at the table of their employers. Can as much, on the score of equality, be said of the North? With us the two great divisions of society are not the rich and poor, but white and black; and all the former, the poor as well as the rich, belong to the upper class, and are respected and treated as equals, if honest and industrious; and hence have a position and pride of character of which neither poverty nor misfortune can deprive them.

I think that based on this evidence, and the fact that actual experts seem to largely agree that the codification of race in the legal codes of the colonies and then the united states were based on realpolitik, with consideration given to economic and political power these laws gave to the elite classes, which is then justified by and grounded in racist theory and rhetoric, which developed and changed over time in order to support the existing hierarchy. That said, I haven't actually been able to find whether any of the actors who put these initial policies in place (e.g. the Virginia Slave Acts) ever actually wrote about their motivations and said 'yes, Bacon's Rebellion was a problem".

I'm positive there's more to say on the subject of the social construction and justification of race and class, and the actual history of racism and classism in the USA, but I hope this gives a brief sense of how racialized thinking might become part of a prevailing ideology which reinforces (and is reinforced by!) practical legal and social structures.

A People's History of the United States is probably the single most popular 'bottom-up' historical book ever sold. Zinn's writing has been criticized before by historians from both sides of the political spectrum for the 'Marxist' lens in which it views American history. That does not mean that A People's History does not make some legitimate claims about race, how the modern idea of race was constructed/defined in colonial America, and how that construction led to the continued enslavement of Africans and African Americans until 1865. I personally find it a useful book for introductory history and how to analyze what lenses people may be using (Marxism, feminism, etc).

To answer that question, I think it makes more sense to go back to before the 1760s from your Zinn quotation. As many Americans know more widely now (since the publication of the NYT 1619 project), the first African slaves arrived on colonial soil in Virginia in 1619. At this point, the idea of race as to how we view it today had yet to truly become formulated or solidified (or even codified), but there are primary sources that show that Africans were recorded as 'Negroes' in censuses, showing that they were viewed as different from their white counterparts. While there is an immense amount of literature about the creation of race in America from social historians, it is widely accepted that these ideas began to formulate shortly after the importation of these enslaved Africans in 1619, at least in America (remember that enslaved Africans had reached the Caribbean almost 100 years prior to this 1619 date in Virginia). It is a historical fact that white indentured servants were used for manual labor on the colony and that their existence was an extreme hardship. What may be hard to ACTUALLY pinpoint is what precise moment a wealthy landowner thought that "maybe we should separate Africans from the Europeans to create a more unified white supporting base and further subjugate the African people."

What we can look at is the idea of "that which comes forth follows the womb", that is the idea of partus sequitur ventrem in the colonies. This laid out the legal framework in Virginia in 1662 that children born to enslaved Africans inherited their mother's status as an enslaved person. This was in contrast to established British law where the male was the head of the family and thus the kids inherited the father's 'status' (as a free person). This law served two purposes (both morbid): it laid the groundwork for the idea of blackness being associated with enslavement and thus free labor and provided a renewable workforce as the children grew older.

Colony life was hard and often times bringing in indentured servants from Europe could prove difficult, inconsistent, or challenging because of the ability for people of similar languages, cultures, and backgrounds to demand more, escape, rebel, etc. It was less difficult to import and purchase African slaves, who oftentimes did not speak the same language as their African counterparts, were different culturally or ethnically. While the Gold Coast was known for its exportation of enslaved Africans, often these people were not all from the same regions of Africa. This can be seen as a valuable way to break people down and quell rebellions (being in a foreign land, away from kinship bonds, etc).

Que Bacon's Rebellion in 1676 in which enslaved whites, Africans, and indentured servants rebelled against the ruling elites of Virginia. From an elite standpoint, as enslaved Africans and African laborers continued to create a larger portion of the workforce, it would make sense (from the elite planter's point of view) that they should be more fearful of a united lower-class revolt that was made up of all oppressed groups. Historian Alden Vaughan writes that " The benign situation of free blacks ended soon after Bacon's Rebellion. Breen and Innes assert that the sharp increase in slave imports, especially of unacculturated Africans, "exacerbated racial tensions" tensions whose existence the authors had heretofore largely denied. Whites began for the first time to discuss black inferiority because the importations "generated racist ideas or brought to the surface latent racist assumptions." Free blacks suffered as much as the newly imported slaves. Some black farmers moved to Maryland in search of better land. Those who stayed in Virginia faced declining prosperity, and 'increasingly their white neighbors treated them with distrust and disdain. In 1699 the legislature ordered free blacks to depart the colony within 6 months."

Shortly after that, the law known as "Of Servants and Slaves in Virginia" was passed in 1705 that further separated Africans from white Europeans and gave greater control to the enslavers. One part of the law stated that "That whatsoever English or other white man or woman, being free, shall intermarry with a negro or mulatto man or woman, bond or free, shall by judgment of the county court be committed to prison and there remain during the space of six months, without bail or mainprize; and shall forfeit and pay ten pounds current money of Virginia, to the use of the parish." This demonstrates the ideas of the inferiority of the African people manifesting themselves into codified law.

While this response was longer than I intended, I think it provides a brief overview of how you could argue that it was indeed within the grasp of the planter elites to begin separating enslaved Africans, enslaved whites, and their indentured counterparts well before the 1760s. This also provides credence towards Howard Zinn's argument that is was still within the interest of the established elites in revolutionary America to maintain that racial status quo. Britain even recognized this vulnerability and promised Africans in the colonies citizenship if they fought against the American rebels. Many of these veterans were relocated to Nova Scotia and surrounding areas after the war by England. Additionally, the formulation of the idea of race and thus racism in colonial America is an extremely complicated topic and one that we could write our dissertations on, but I hope this served as a good introduction to your question.

Sources:
Vaughan, Alden T. "The Origins Debate: Slavery and Racism in Seventeenth-Century Virginia." The Virginia Magazine of History and Biography 97, no. 3 (1989): 311-54. Accessed July 7, 2020. www.jstor.org/stable/4249092.

Cohen, Robert. "THE SECOND WORST HISTORY BOOK IN PRINT? RETHINKING "A PEOPLE'S HISTORY OF THE UNITED STATES"." Reviews in American History 42, no. 2 (2014): 197-206. Accessed July 7, 2020. www.jstor.org/stable/43661655.

Mahmud, Tayyab. " Colonialism and Modern Constructions of Race: A Preliminary Inquiry"

Burawoy, Michael. "Race, Class and Colonialism".

Morrock, Richard. "Heritage of Strife: The Effects of Colonialist "Divide and Rule" Strategy upon the Colonized Peoples." Science & Society 37, no. 2 (1973): 129-51. Accessed July 7, 2020. www.jstor.org/stable/40401707.

Further reading on ideas of race, African enslavement across the Americas (Latin America, the Caribbean, North America):

Roberts, Neil. Freedom as Marronage. Chicago, IL: University of Chicago Press, 2015

Sweet, James. Recreating Africa.

Eller, Anne. We Dream Together: Dominican Independence, Haiti, and the Fight for Caribbean Freedom.

Stevenson, Brenda. What is Slavery?

Gossett, Thomas. Race: The History of an Idea in America

While in some parts he is factual, I would be extremely cautious taking anything (particularly concepts) from that work. His explanation of how the Pilgrams arrived and immediately began to massacre the Pequot to expand land holdings aren't simplistic; they're bad history and are flat out incorrect. His book continues on in such a way of glossed over cherry picking that it becomes difficult without cross reference to determine actual from speculative. His use of concepts like they had sticks, they had rocks, so that means they knew what axes were are likewise misleading at best. His description of Bacons Rebellion, for instance, searches high and low to indicate it was Jamestown forcing poor folks into the frontier, abandoning their pleas for help, then feeling shocked when Bacon pulls himself up by his bootstraps to go handle it for the fronitersmen- then makes a casual reference about Bacon - who had lands - "probably" being more interested in native killing anyway. He searches for the question to which he already "knows" the answer. But that's not how studying history works, that's how op-eds work.

His description of Jamestown "importing the first slaves in 1619" is just as misinforming as the project by the same name. He says the slave trade started in about 1542 when a group of 10 slaves were taken to Lisbon, which is also overglossing but is at least somewhat accurate. The ATLANTIC trade, as Turks and Moors had been trading slaves with Europeans already, started when Portuguese trader Antao Goncalves kidnapped west Africans and returned with them. About a decade later, Pope Nicolas V gave permission to the Portuguese to;

to invade, search out, capture, vanquish, and subdue all Saracens and pagans whatsoever …[and] to reduce their persons to perpetual slavery, and to apply and appropriate to himself and his successors the kingdoms, dukedoms, counties, principalities, dominions, possessions, and goods, and to convert them to his and their use and profit

Then in 1619 a Portuguese ship raided and enslaved Africans. They set sail to sell their cargo in New Spain but were challenged by two British privateers. One would take several of the enslaved passengers, later sailing to Jamestown and attempting to trade for supplies. At this point they entered into indentured servitude - not slavery, which was not legal in Virginia yet (and wouldnt be for another 40 years). But this doesn't stop Zinn from incorrectly claiming the "starving and desperate" colonists were eager to find anyone to enslave for their own survival after facing a very hard winter 10 years earlier and turned to those of a different color out of racism. He also forgives slavery in Africa as what "most of the European population" experienced at the same time. He goes on to claim, while speaking of the colonies, that "10 to 15 million slaves" were brought to "the Americas" by 1800, but fails to include the massive percentage Spanish and Portuguese sent to South America. Visually this represents 12,500,000 - the middle of his claim;

×××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××××

Visually this represents enslaved Africans brought to what would become America;

××××

(And that's an over-estimate sourced from an actual historian and professor focusing on slavery in America)

He then takes his cherry picked information to claim things like;

And to bind that loyalty with something more powerful... the ruling group found... that the language of liberty and equality... could unite just enough whites to fight a Revolution... without ending slavery and inequality.

Which does not fit real time lines. The elite wanted to create chaos so they inspired Parliament to overreact to protests on taxes, leading to dissolution of governments controlled by those colonial elite so they could inspire a war to perpetuate a system already in existence? Nope, bad history.

It has been proposed in more than one state to prohibit its inclusion in any educational facilities, curricula, or materials due to the innacuricies of the work (which some other historians do defend some of, to be fair).

I tend to take the law approach - once you make a bold faced lie, your credibility is extremely reduced and no longer relevant to debate. He certainly made several in this book. I would not read it nor encourage others to without first reading numerous quality works and am skeptical of his conclusions, including the one you presented.