At my age and having lived my whole life in the post-WWII United States, my preference is to maintain American democracy the way it's always been. I like the Constitutional position on government establishment of religion, also commonly known as separation of church and state.
Bottom line: Private religious schools receiving any type of government funding (taxpayer dollars) should be required to comply with the same federal and state regulations as public schools. If they refuse to follow the same rules as public schools, then the revenue flow from taxpayers should be ended and churches should handle the school expenses.
If private schools want their student bodies on their knees every day, praying to whichever deity their religion worships, that's fine as long as the affiliated religion (and tuition fees) are responsible for all operational funding.
Added 2:23 PM Wednesday: Decent Americans were handed some unusually positive political news yesterday, after Felon Mush failed to bribe his way to an election outcome in Wisconsin that he really wanted. The news today includes reporting that Mush could very well be reaching the end of his tenure as Pussydent 47B. Decent people need to hope he's on the way out, since all he's doing now is making Pussydent 47A a whole lot worse than he might be without Mush to handle much of the really ugly shit.