This is a great question and one that is actually quite complicated and dynamic. While you are partly correct that hostilities towards Catholics rose in the 19th century as Catholic immigrants came to America, the foundations of those hostilities are actually centuries earlier. But to put it simply, Catholics were viewed as being too dependent on the Pope's guidance and too wrapped up in their own Dogma to be considered true Christians. Because they have almost always been minorities, repressing their rights have been relatively easy to do. I'll give a brief description around your question, but in order to make this answer not be the length of a chapter in a book, I will give specific examples set in America's first colony that was intended to be a haven for Catholics -- Maryland.

Religious diversity and contention were deeply imbedded in the very founding of states like Maryland as a British colony. As a colony, Baltimore was founded in the early 17th century as a refuge for Catholics who were fleeing restrictions within England. But Baltimore as a safe refuge for Catholics didn't last for long. By the middle of 1600s, it became evident that new waves of immigrants (particularly Anglicans) were now clashing with the Catholics in the colony, so some sort of protections for Catholics were necessary. This was needed because more settlers from England, who belonged overwhelmingly to the Church of England now threatened their rights to worship their God on their own terms. As such, Lord Baltimore created the “Maryland Toleration Act” in 1649, which attempted to create religious laws that were meant to define Baltimore and Maryland as a haven for all Christians of all denominations. However these protections to follow one's own religion of choice did not last for very long.

By 1688, a revolution within Maryland put an end to religious toleration. Even more challenging for minorities like Catholics is that by 1707 the Church of England became the official state church of Maryland, with heavy restrictions against non-Anglicans (Thomas O'Brian Hanley. The American Revolution and Religion: Maryland 1770--1800. The Catholic University of American Press. 1971. Pp 7). These restrictions came in many forms, but included priests being forced to return to England and Europe and the closing/burning of their churches. Worse, is that as time crept through the 18th century, Catholics saw themselves become targeted even harsher with taxes being levied against them.[Hanley. Pp 110]. This, needless to say, began to really spark contempt for the Anglican Church by Catholics within Maryland.

The American Revolution really changed the way Catholics were viewed in many states. This is partly attributed to people like Charles Carroll of Carrolton, who was one of Maryland's delegates at the Constitutional Convention, signer of the Declaration of Independence and a Catholic. Carroll and his family had watched for years as Catholics were persecuted, and they had had enough. In the years leading up to the Revolution, Carroll wrote editorials in the Maryland Gazette, arguing that Catholics were just as Christian as Protestants and that they should be allowed to worship in their own way. Critics, such as Daniel Delaney (a Maryland politician), outright used hate speech in his condemning tone towards Catholics. The term he and others used were "Papists" and said that they had no right being a part of the US government or worshiping in their own way because they answer to the Pope, and that is a sin. The two of them ended up entering an intense series of dialogues in the Maryland Gazette throughout 1773 known as the "Antilon-First Citizen Debates"

The Antilon-First Citizen Debates were a series of exchanges between Anglican Daniel Dulany and Charles Carroll of Carrolton in the Maryland Gazette that took place on the eve of the Revolution in 1773. It started with Dulany writing a theoretical debate between a First Citizen, who was Catholic, and a Second Citizen, soon to be known as Antilon who was Protestant. Dulany sought to attack the First Citizen for being a “papist”, who’s own allegiance would be to the Pope, not to Democracy. Even more outrageous according to Carroll, was that Dulany was defending the Governor’s right to impose taxes on Maryland residents without going through the state legislature. Outraged by this, Charles Carroll struck back, and argued against this in his own fictitious debate. The two exchanged a total of seven letters, all of which can be found within: Onuf, Peter. Maryland and the Empire: 1773: The Antilon-First Citizen Letters. Johns Hopkins University Press. Baltimore. 1973

These letters are incredibly detailed and long, and they do not entirely have to do with our theme of Religion during the American Revolution. Rather, what we will see is that Dulany attacks The First Citizen for his Catholic views as a form of slander, and we will eventually see that Charles Carroll will bring in Catholic-based issues to defend the injustices that faced people of his particular religion. What is important to realize is, this debate propelled Carroll’s popularity forward, and displayed for Marylanders the very fact that a Catholic can stand up for liberty and justice.

Long story short, Catholics over-whelming supported the Revolution, which resulted in them earning their own religious freedoms through the creation of constitutions like Maryland's in 1776, which got rid of the taxes against them and allowed them to open their own churches once again. It didn't fix all the problems (Catholics would continued to be harshly judged and slandered for centuries to come) however, it at least protected their own rights moving forward