So not really Fascism (as you loose some power to the Church, something Mussolini refused to do), but but radical Christianity with fascist ideals (a motherland instead of a nation, you only exist through your work, the only people that matters is you and your family, stuff like that).

It didn't work great with catholics (i mean, without US state dpt, you'd have a lot less fascism in South america), because of all the cardinals and the pope, whil not the best human beings, are at least decent ones. Fascism have a hard time building power on catholicism in general, because the church power is in the Vatican, which is tolarable if you're Italian, but harder to use if you're not. You can see that during Bolsonaro authoritarian drift at the end, he was suddenly a lot less christian than he used to be when attacking gay rights and abortion rights, and wasn't able to capitalize on the church power anymore.

Historically Christofascism didn't perform great. Might be different in a non-catholic country.

Or just to prevent their children from being infected by "worldly values". You'll often hear them say "Be in the world, but not of the world."

There are of course, people who do it to give their children an education that they feel is superior to the regular one, but they are a minority.

Of course, I didn't survey all homeschoolers to come up with that, I suspect you'd find clusters of secular homeschoolers in certain areas on the west coast, but elsewhere, Jesus dominates.