Alvin Toffler called it back in the 70s (in Future Shock); in there, he thought educated elites would move towards homeschooling, nothing political on his analysis at least (that may match current trend?)

There's nothing inherently right-wing about homeschooling. You could just as easily homeschool as left-wing parents who don't want your kids immersed in an environment where other kids judge them by what brands they're wearing, and where the teachers all subscribe to the capitalist view of how society should function.

It's true that homeschooling has been more prevalent among the right wing, but there are lots of people who do it for lots of reasons. We did it when our local elementary school was bottom third in the state. My wife called up the vice principal, and asked why we should put our kids in their school. He said that their school could toughen up our kids. We decided that "tough" wasn't our main goal for our daughters, and we noped out of that school.