He's exaggerating (for the US), but I think what he's getting at is that at this point the schools are pretty well liberal unless they're private. So a lot of home schoolers are of the conservative set and liberals might not like that and try to interfere.

For example Billies kids might, in addition to the three R's, learn "To shot cocksuckers that try to take their guns". Probably some other stuff. So if that got out I could see some liberals at least wanting to intervene somehow.