Even though the Free Masons and the Catholic Church are supposed to be sworn enemies that hasn't stopped people like Jack Chick from conflating the two. So I was wondering if his 19th century counterparts in the Anti-Masonic and Know-Nothing movements also did something similar
I'm probably in violation of the rules here, but I can point you to what looks like a possible well-informed source: Holt, Michael F. "The Antimasonic and Know Nothing Parties", in Arthur Schlesinger Jr., ed., History of United States Political Parties (1973) which may have some insights.
As a Mason, but not a Catholic, I can say that we've pretty much always had a fair leavening of Catholic members - the RCC may officially declare us off limits, but we do not reciprocate the ban.
/u/cryptoengineer makes some good points, but I just want to add that the Know Nothings were established in 1845 while the Anti-Masonic party was dissolved in 1838, so the overlap between the two movements doesn't seem likely to have been significant if it existed at all.
Anti-Catholic sentiment in the US was also not new to the 19th century, where anti-Masonic sentiment had existed in some corners previously, but was never very significant pior to the early part of the 19th century, not merely in response to the Morgan Affair, but certainly proximate to it.
Further reading: