Ideally yes. But in fact the state has already swallowed much of the personal sphere. Thus one is hard pressed to protect their personal interests without appealing to the state.
For example, consider the perspective of a right wing Christian who after being forced to pay for public education may not have money left over to send their child to a private Christian school. Predictably this puts them at odds with their atheist neighbor who is also forced to pay for the public school. The school curriculum, policies regarding prayer, ethics, and sex education are all now in both the sphere of the personal and of the state and will directly impact the lives of both their children.
Until this changes, it is not reasonable to single out the Christian right as being the ones who must lay down arms and play dead in those parts of the culture war that the state has taken over.
I don’t see how your tax-paying right-wing Christian’s situation is any different than a person who prefers private school or somebody who has no school age children. The school tax taxes them all, just the same as the person who enrolls his children in public school.
Should a childless person get a rebate? If not, then why should the right-wing Christian?
I send my children to Catholic school and gladly pay the bill. If I couldn’t, after paying the ridiculous school taxes in my town, the Catholic school offers help.
Frankly, I do not support public education. It is far to sensitive a matter to be handled by the state. It would be far preferable if there were no school taxes whatsoever, and people were responsible for the education of their own children. Failing that, I support vouchers.