In Michigan, it is prohibited by our state constitution for tax money to go to religious and private schools. So Betsy Devos pushed the "charter school" movement to create pseudo-private academies but call them public schools because they are chartered by state universities. But there is little oversight. The charter movement here in Michigan isn't just a supremacy thing- it's a "funnel tax dollars to the wealthy" thing, given that Heritage Academies is owned by JC Huizenga and his charters are profit making schools!
But great summary of the history - we (the USA) aren't out of it yet.