I say I agree with you and welcome to the real world. They see it one way and that is there way. School boards by me are made up of parents that have kids in public schools no matter the make up of the community. There are never ending fights over control between different groups with kids in public schools.
Their view is you want to send your kids to private schools then pay for it yourself. I did.
First of all, you seem to think that all PS boards are always made up exclusively of PS parents. This is definitely not true. Retirees, people without children, etc. get elected to boards all the time for the same reason - curb spending/taxes. We (and same for the aforementioned non-PS parents) are not saying we shouldn't contribute at all to the PS system, but we should have a say in the budget.
As far as paying for private schools - WE DO!!!! Of course we do. The amount of money private school kids get from the local school district (for busing and other services) is a small portion of the total cost of education, and pales in comparison to what is spent on a per child basis for PS.
ETA: And we understand the perspective of the PS parents - what we don't understand is the level of hate that comes with it.