When this country was founded, the church was the center of a community. And our founders, in the first amendment, said that the federal government can never intrude on that relationship.
Had they been writing that constitution now, they would put the same restriction on the education of our young people - the federal government has no place in that setting.
They would have put this in their state constitutions, as well as county,city, and town charters as well.
If our Founding Fathers could see the effects of government interference in education ( regardless of how local) they would be horrified.
Fundamentally, it is impossible to have a religiously, politically, or culturally neutral education. When one neighbor can use the government ( regardless of how local) to force another neighbor to fund their philosophic worldview, then we have tyranny of the voting mob over the hearts and minds of children and their parents.
Government schools are a First Amendment and freedom of conscience abomination!