In a Jewish educational system, parents are not baalei batim on chinuch, even though they pay and support the yeshiva – rabbis are bettee equipped and qualified to decide what to teach, and parents who are not interested are able to simply find a different school, and then proceed to support that institution and its rabbis; in neither case is the parent influencing the school itself. But to demand payment from parents who do not send their kids to the school is baseless.
Logically, if one is obligated as a tax payer to support the schools, they should have a say in how the school is run, even if due to their personal beliefs they are forced to send their kids to private school. If they don’t want parents to have a say in how the school is managed, they should allow a tax rebate for parents who opt out of the system and have their children attend private or home schooling. That way, the public school can say “this is how we want to run the school – if you don’t like it, take your children elsewhere”.
That’s all regarding mere disagreements. When the issue is the degeneration and upheaval of all foundations of civilization, it becomes an issue that affects the entire society, even people who don’t have school aged children. If a school decides to teach children to be murderers for instance, that has an impact on me no matter what my personal stake is in the institution, because I’m going to have to live with the unfortunate souls who will be the product of that education