All with different interpretations of the Christian god (or not Christian, as in the Jewish diaspora). The Spanish who settled colonies in Florida and California, the French in Louisiana, the English, Polish, and German settlers in Jamestown would all struggle to agree on a common set of definitions or rituals except there was a bible in there somewhere.

I was led in prayer at public schools, and private - doesn’t mean I or most of the other students were religious, though some were. And that is a very recent thing. Most regions didn’t have public school bible reading then.

You seem to be making a statement that the US has some strong theocratic religious foundation, when it’s more of a ‘we’ve got too many competing groups that can’t get along with each other - we’ll just kinda stay out of it where we can’. Hence the hand waves part. Which is good, we’ve never had the religious wars where a specific group had to fight against another, which is how you end up with the state religions like in Europe (anglicans vs Catholics vs Protestants for instance).

The groups you’re pointing to were often refugees from those fights and came in as waves during the various periods of repression as tides turned, or different regions fell to famine.