Let's also not forget that early in our existance, there were communities that were largely one faith or the other and the institutions in those areas reflected that predominate faith. Jewish and Catholic come to mind, but I'm sure there were protestant situations also. And of course in Utah, prior to mass migration, if you weren't Mormon, you weren't anybody and had limited rights as the jobs, schools and courts had a decidedly Mormon bent. As I mentioned earlier, I remember back in the 80's when the Moonies tried to take over a region. I don't know what became of it.
America is soul searching now and it's not beyond the realm of possibility that there are those who could given the right tools and set of circumstances push forward a theocratic agenda. Frankly, even though he keeps getting soundly defeated, you would probably find such a person in Alan Keyes.
If you see a case of that, ping me to it.