While I think this is a sad situation, I am not necesserily compelled to give.
I don’t believe that sending your kids to a slightly less religious school (I’m not talking about going from BYOBP to Flatbush or anything) warrants pekuach nefesh. If your kids can’t handle a slight change in hashkafa, perhaps the education wasn’t worth a penny anyway.
Home schooling is always an option. Most of the parents of BYOBP are learned enough to teach their children. They could always pay the rabbonim directly for tutoring for the older, more advanced kids.
Or, small groups can get together and CO-OP.
I would rather donate to feeding people. If you don’t eat, you can’t learn. If you have something to eat, you can find a way to learn.