“(I don’t see why it makes a difference if the school is for boys or girls, but that may be in the funding structure).”
It was – most Chareidim send their boys to schools that are completely private and their girls to Bais Yaakovs which are partially funded by the government, although there are also many Chareidim who send their girls to completely private schools as well (perhaps for this very reason – there is less government control).