You haven't followed the arguments or accepted that what the (R) are saying is often what they mean. That's the first point. If there were a federal property tax you'd hear it.
Moreover, property taxes are set very locally and they see the results. All kids get essentially, they like to think, the same services in a given district. Even the kids of poor parents.
They don't like income redistribution. If they agree to pay higher taxes for their schools they object to having a portion of it siphoned off for other districts. That creates push back from time to time--why raise taxes if it doesn't help those you want to help? This created well-funded PTOs and some districts have forbidden PTOs from helping their school too much; if the PTO raises too much money, then it's taken and given to a poorer school.
They've been paying taxes for education for so long it's like they're broken to the saddle. In fact, in many places they're willing to pay more for education than they do now.
In many cases they like vouchers. They pay for their kids' education, not just generic "taxes." Then, if you don't send your kid to the public school for some reason, they expect you to pay for public school and private school. Not the extreme disagreement with SpEd: If the local school doesn't offer services that are required, you can make the local school pay for very expensive private services to be provided. This is often considered "progressive," but the same thing, for less money, for "normals" is regressive.