You have it partly right.
American history does move in cycles.
Observe this attitude toward immigrants and immigration:
As immigration from Europe and Asia neared its crest in the late 19th century, anti-immigrant sentiment soared along with it. The U.S. was in the grips of an economic depression, and immigrants were blamed for taking American jobs. At the same time, racialist theories circulated in the press, advancing pseudo scientific theories that alleged that “Mediterranean†types were inherently inferior to people of northern European heritage. Drawings and songs caricaturing the new immigrants as childlike, criminal, or subhuman became sadly commonplace. One 1891 cartoon claimed that “If immigration was properly restricted, you would never be troubled with anarchism, socialism, the Mafia and such kindred evils!â€
Ethnic bigotry.
I was born in the 1950s. I remember Protestant neighbors maintaining that Catholics were a hazard to American democracy because Catholics had no alleigence to America, exactly the same as you just said with your remark about the Pope relocating to Florida. I even took them down into the basement of St. John's Church to show them that we kept no arsenal down there. (Boy, would I have gotten in trouble if Father Tom had found us!) But they didn't believe me. They claimed the weapons were hidden someplace else. I have no doubt you will make the same claim.
Religious bigotry.
We always find someone new to blame our troubles on when we're afraid. You forget that American national identity isn't transmitted by blood. It's an idea. When we welcome those who come, we transmit that idea, if not to them, then to their children. It's viral. The only way to keep such an infectious idea from spreading is to quarantine the uninfected. Yet, in cycle after cycle, we seek to do that, and make the same mistake, again and again.