Not exactly. The motivation to leave Europe is right in the Constitution if you look at it carefully enough. The whole church of England (or whatever country) thing was their big problem. They wanted to go somewhere that they didn't have a mandatory church so everyone would be free to practice whatever religion they want. At the time if the church of England was Catholic and you were Protestant, there would be problems (and vice versa).

I'm not sure that the founding fathers really considered that having no religion was also valid, and that having a non-Christian religion was also valid, but that's exactly the ideas they tried to enshrine in the Constitution.

The right wing nutjobs wanting to make their religious beliefs into law would be dissidents when the United States signed that piece of paper declaring themselves as a new country. IMO, they still are, and bluntly, they should go. If they're not willing to be tolerant of other faiths, then they're being rather un-American.