My parents went to public schools, and got great educations. Those schools were government schools, and nearly every administrator was a Democrat, as was just about every state politician. Something must have happened.
Fedgov money, then it all became a political game.
Without apologies: Marxism and Cultural Marxism after it happened (the parents for political correctness etc).
Or, as I sometimes observe, there’s a reason why scum like Bill Ayers went into teaching teachers.
Likewise I could point you to School of Darkness by Bella Dodd, available in PDF form online.
There is a distinction because Marxist create Cultural Marxist so that the latter may tear down and destroy a society and a civilization, not that they may be the revolution but so that they may be swept away in it, used up as Cannon fodder.
Actual Marxist, though their ideology is debased and utterly wrong, still want to build a society that can sustain itself for the long haul so they often don’t tolerate the kinds of crap that Cultural Marxist outright champion.