I don't think anyone could establish theocratic rule in this country. If it didn't happen when the country was nearly all completely Christian, why would it happen today, when the country has the most religious diversity its ever had?
Uh, because those Christians actually believed in separation of church and state and disestablished the state religion. Also, even Christianity itself was split into many different churches that feared being dominated by others, like the Baptists and Catholics, who were often oppressed in the colonies. Nowadays, these divisions within American Christianity have been de-emphasized for various reasons, so it's viewed as more of a united front than it ever has been.
It's not much different today. The overwhelming majority of Christians, both liberal and comservative, believes in the separation of church and state. It is a very loud yet small minority that believes otherwise.