At least where I’m from, the majority of homeschooled children are in conservative Christian (or Mormon) families, with a minority (but still notable) in super-left-wing hippy families. Very, very few in non-extreme families.
As purely anecdotical data, where I'm from it's actually the opposite, majority hippies, vegan, alternative/free education advocates, etc, and a minority of mostly morally-concerned non-left-leaning (mainly religious) people, as well as specific cases of children with special needs that simply can't adapt to public education because of external reasons (bullies).
As a matter of fact, the hardcore religious right in my country have their own private education institutions, which are quite powerful themselves.
So even the (non-catholic) Christians who homeschool because of religious and moral convictions end up being moderate/center people trying to move away from both extremes.