Just thinking out loud: The people of the city/county/states should be free to decide how they wish to run their schools. Same for people that wish to set up their own private schools. I want there to be choices and competition among options. We should be free to decide where we wish to place our kids and we should do our homework before selecting a place to live. I want people to have the freedom, if they so choose, to live in a place more closely aligned with their values. I don't necessarily want to force my preference of vax/no-vax on your school. We should bear the weight of our decisions.
Let's talk about the idea of "people being free to decide how they wish to run their schools." This is actually the opposite of individual freedom. What this actually implies is that the majority should be "free" to run over the rights of the minority. The majority is "free" to demand compulsory education and "free" to dictate personal medical decisions.
So because of this collective "freedom," the individual discovers that his personal, medical, and educational decisions are being dictated by force. This is unjust.
You mentioned private schools. That is the only legitimate place where the owners can impose such rules. Why? Because it is an exclusive, voluntary institution. No one is forced to be there and only the owner decides who is allowed there. People who want to be surrounded by vaccines should embrace private schools as their sanctuary.
Public schools, on the other hand, are owned by everyone and may not be exclusive. Not in a free and just society, anyway.