Most Catholic churches have their own schools and if they would have to pay property taxes this could force them to close.
Not just Catholics, but almost every major denomination has their own schools. 10’s of thousands of them.
There are ways around that. Most schools are listed as separate corporations. A parish could drop the 503C status (in theory) while the school keeps it. Schools don’t perform marriages, and the religious clause has been held up in court for them.