Actually the school is a chinuch atzmai school. Chinuch Atzmai is partially funded by the gov. not fully as a compromise that they should be allowed to run the schools how they wish and so that their schools are not public schools which have to accept anyone who applies.
Also it’s not an issue of the gov funding. these parents took their girls out of the school and sent them to bnei brak but the court is forcing them to go back to their original school.