There is an implicit assumption in the question that there was a shyness about speaking racist notions out loud. This was not generally the case.

Consider: Carter Glass, member of the Virginia Senate (and future Secretary of the Treasury for Wilson). In 1901, at a Virginia Constitutional Convention, he proposed a poll tax. $1.50 required payment to be eligible to vote; the tactic had already been successful in other states in removing large chunks of the black electorate. The first to the poll tax was Georgia in 1877; the result was having an estimated 38% black turnout in 1884 drop to 19% in 1888.

By fraud, no; by discrimination, yes. But it will be discrimination within the letter of the law, and not in violation of the law. Discrimination! Why that is precisely what we propose; that exactly is what this convention was elected for – to discriminate to the very extremity permissible under the limitations of the Federal Constitution with a view to the elimination of every Negro voter who can be gotten rid of, legally, without materially impairing the numerical strength of the white electorate ...

The whole list of proposed clauses included a property clause, literacy test, and grandfather clause in the debate, but it led to major disagreement -- mainly not because of disenfranchising blacks, but because some solutions would also disenfranchise whites (too many whites would be hit with a “you must own property" clause). There was great effort put into working out a way to only disenfranchise blacks with any particular rule. The eventual compromise was the poll tax already mentioned, plus an "understanding clause" (essentially, a literacy test involving understanding a portion of the Constitution).

Or jump forward in time, and consider an 1944 academic paper by Donald S. Strong. He traces the reasons for and against a polling tax, and mentions

Belief in the poll tax is socially correct in the South. Logical argument is only a minor bulwark of the tax. Its main defense is the raised eyebrows that follow any questioning of the wisdom of this voting requirement.

And later gives, as reason #1 for the tax: that it is "essential to white supremacy" and mentions "whispered justifications" that "the n****** outnumber the whites in Texas".

The paper points out how wrong that reasoning is, due to the states which have abolished poll taxes but haven't seen black turnout budge much, by the simple expedient of a different tactic: making the Democratic primary be whites-only. The paper also makes historical errors and is generally racist -- 1944, remember -- but it's correct on this point.

8 states -- all them from the Deep South -- adopted white primary laws around the turn of the century. As the Democrats were dominant in those states -- this is before the Southern strategy reversal of R and D -- preventing blacks from voting in the party vote was essentially equivalent to preventing them from voting in the main election.

We're not talking some sort of sideways-language here. Here's a resolution adopted May 24, 1932, by the Democratic party of Texas.

Be it resolved, that all white citizens of the State of Texas who are qualified to vote under the Constitution and laws of the state shall be eligible to membership in the Democratic party and as such entitled to participate in its deliberations.

Yes, it straight up states: you have to be white to vote. They even got away with this for a time; in Grovey v. Townsend, a case against the resolution went to the Supreme Court in 1935, and the Supreme Court upheld the constitutionality. (There were prior attempts which were thrown out because they were based on state rules, and violated the Constitution; the state delegated to the rules to the parties in response, and since the parties were "private" they were allowed to discriminate.) This was shut down again in another 1944 case that was technically narrow (that is, it could be argued to only apply to Texas) but this tactic was phased out afterwards.

Of course, states got to hold on to their other Jim Crow laws post-1944, like literacy tests; here's a sample from 1964 of a "practice test" used by the NAACP to assist those wanting to vote in Alabama. The registrars graded it to their discretion (you can guess who they graded harder).

The most infamous test is the Lousiana one, with 30 deceptive multiple choice questions where getting a single one wrong invalidates the test. There's also a portion requiring interpreting part of the US Constitution.

If you were black, you might get a section like:

Full Faith and Credit shall be given in each State to the public Acts, Records, and judicial Proceedings of every other State. And the Congress may by general Laws prescribe the Manner in which such Acts, Records and Proceedings shall be proved, and the Effect thereof.

if you were white:

Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the Government for a redress of grievances.

There was no secret at all to the purpose of the laws. Things weren't really deconstructed until the Voting Rights Act of 1965, where the last ditch-argument trying to prevent it surrounded not justifying the practice but just attacking the constitutionality of the law, example:

[This bill] is patently unconstitutional. It has an indefensible intrusion by the Federal government into an area where it has no constitutional right.

and the same letter faintly frets over how passing the law is somehow like Hitler.

The German nation did exactly the same thing in the thirties, at a much more rapid rate, to be sure. But make no mistake about it, the United States of America in the decade of the sixties has taken the same road.

The bill -- after some amending -- passed the House 328-74 and the Senate 79-18. Martin Luther King Jr. and Rosa Parks both attended the signing in August 1965.

...

Berrey, S. A. (2015). The Jim Crow routine: Everyday performances of race, civil rights, and segregation in Mississippi. UNC Press Books.

Grovey v. Townsend, 295 US 45 (1935).

Holt, W. (1968). The Virginia Constitutional Convention of 1901-1902: A Reform Movement Which Lacked Substance. The Virginia Magazine of History and Biography, 76(1), 67-102.

Kousser, J. M. (1974). The shaping of southern politics: Suffrage restriction and the establishment of the one-party south, 1880-1910 (Vol. 102). Yale University Press.

Packard, J. M. (2003). American Nightmare: The History of Jim Crow. Macmillan.

Strong, D. (1944). American Government and Politics: The Poll Tax: The Case of Texas. The American Political Science Review, 38(4), 693-709.

There is a quote from James Baldwin in his book Down at the Cross that says, "The only thing that white people have that black people need, or should want, is power-and no one holds power forever." That quote aptly sums up why Reconstruction, Black Codes, and Jim Crow were so harshly defended in post-Confederacy America. There was a racial hierarchy that had to be defended and losing the Civil War threatened that immensely. Confederate defeat and the brief period of Reconstruction did not overturn that racial hierarchy. It was maintained differently though, in court than it was by citizens in public. Not that their intentions were any different, as the wording only had to be slightly modified in order to get the federal government to look the other way.

In 1883, for example, the Supreme Court ruled that the Civil Rights Act of 1875 was unconstitutional because it was argued that Congress did not have the right to enforce laws meant for the state on private individuals. As in, Congress had the authority granted to it by the states and federal government to enforce the 13th and 14th Amendments at the state level, but not to force private businesses to accept African Americans as patrons to their businesses. So, we can see how lawyers could win in court by arguing that it was a matter of private rights to be racist, not the state, and how would the government have the authority to determine what is a private act of racial discrimination?

Thus, it was argued in Plessy V. Ferguson in 1896 that providing separate areas of African Americans still satisfied the 14th Amendment. It wouldn't be until 1954 in Brown V. Board of Education that the Supreme Court would overturn that ruling that 'separate education facilities are inherently unequal" (Earl Warren, 1954).

​

Plessy V. Ferguson established that in 1896 that the 'separate but equal' defense was enough to satisfy the 14th Amendment requirements that states had to adopt at the end of the Civil War (one of the three Reconstruction Amendments). The 14th Amendment states, among other things, that "No state shall make or enforce any law which shall abridge the privileges or immunities of citizens of the United States; nor shall any state deprive any person of life, liberty, or property, without due process of law; nor deny to any person within its jurisdiction the equal protection of the laws." There wasn't really a reason to hide the reasoning behind Jim Crow laws in the American South. They evolved from enslavement through the Confederacy into Black Codes into Jim Crow and into the modern-day.

A state like Mississippi could require the passage of voting tests (can you recite or write the state constitution) to vote at the discretion of the white poll runner. As in, they wouldn't ask any white people for proof of literacy but would deny every black individual. These states faced very little push back from the federal government, as they had been hesitant ever since Reconstruction to become overly involved with actively enforcing the Reconstruction Amendments. In short, there wasn't really a political need to hide what their intentions were. The design of white supremacy remained after the Civil War and really did not change for 100 years. Even after the 1964 Civil Rights Act and 1965 Voting Rights Act, white backlash remained (remains) strong.

For books on the 1950s or so/after on Civil Rights, American Conservatism and the defense of racial segregation and Jim Crow:

Mothers of Massive Resistance: White Women and the Politics of White Supremacy by Elizabeth Gillespie McRae
The Politics of Rage: George Wallace, The Origins of New Conservatism, and the Transformation of American Politics by Dan T. Carter
Suburban Warriors: The Origins of the New American Right by Lisa McGirr
One Person, No Vote: How Voter Suppression is Destroying our Democracy by Carol Anderson
I'll add a couple more when I think about it, I'm just forgetting a few right now.

The book Legislating Racism: The Billion Dollar Congress and the Birth of Jim Crow (2004; I summarize pp.102-4) describes the arguments made by Southerners in detail. The most serious justification of voter discrimination was a book called Why the Solid South? (1890) authored by fourteen southern congressmen. Purporting to describe corruption by black and Northern agents, it created a mythology of the "failure of Reconstruction" which lasted until the 1990s. Each chapter of the book deals with an individual state, and each has a "happy ending" which is brought about by the state denying suffrage on the basis of race. None of the laws are described as being racially based, because of the 15th Amendment, but allegations are made, for instance, of non-whites committing voter fraud.

On the other hand, facetious arguments that had nothing to do with race were also common. In response to Senator Henry Cabot Lodge's final attempt to stop these discriminatory laws in 1890, Southern Senators claimed that this was an issue of Northerners imposing "force" on Southerners, how federal election officials would become corrupt and seek private gain in exchange for certifying votes, and how the law was basically despotism. The voting restrictions themselves were also justified along supposedly neutral lines: one of the authors of the 1890 Mississippi Constitution wrote that

The Mississippi Constitution applies equally, and without any discrimination whatever, to both the white and negro races. Any assumption, therefore, that the purpose of the framers of the Constitution was ulterior, and dishonest, is gratuitous and cannot be sustained.

This author also points to the Connecticut Constitution which requires "good moral character" of voters, saying that it's basically the same as the Mississippi Constitution's literacy tests. This "whataboutism" argument was made by several different senators during the debate over the Mississippi Constitution.

Therefore, the authors of the Constitution believed they had provided a standard that did not make a racial test. However, when confronted by Northern protests in the Senate, Senator James Z. George (D-MS) maintained both arguments at once: he simultaneously claimed that the law did not deny suffrage on account of race, and that the purpose of the law was to maintain white supremacy. According to the source linked above, he "declared the great truth that the Anglo-Saxon race would never submit to the domination of an inferior race," but also proclaimed "the fairness and impartiality of all the various franchise clauses of the Mississippi Constitution." (One of the two statues Mississippi has placed in the National Statuary Hall is of Senator George; the other is of Jefferson Davis.)

The governor of Mississippi, James K. Vardaman, reports that Georgia and Louisiana made similarly two-faced arguments, but he was far more straightforward in stating that the Southern laws were about race and only race, saying that the South "arose in the might of Anglo-Saxon superiority and drove the veneered savages from the polls." (Vardaman has a building named after him at the University of Mississippi.)