If you look at it historically in Europe after WWII the churches in dictatorships where captured by the state, some churches more than others but none unaffected. Some churches even agreed with the dictators or otherwise supported them. During the communist dictatorships in East Europe it was common that priests stationed abroad were informing on their constituents.
It's even happening in USA, a democracy, around Donald Trump with the White Evangelical Church that was first was captured by GOP and then deepened under Trump. You're quite insular but there really are things to learn, though that are frightening, and indeed, Europe has some lessons for you. Your Founding Fathers took the lessons at heart when they wrote the Constitution and the Ammendments , and then some. Your Constitution became a model for a number of other countries, including Norway's in 1814 when that was written. They did not follow all of it, sadly, especially about church and state.
Edit: Spelling and grammar.