the Mormons adopted the public schools as their own since they were all Mormons anyway. The other denominations started private schools. So Mormons view public schools as their own and view privates as other denominations. In fact many Utahn's go out of their way to mock anything that is not traditional education they are used to. Which is large public schools. Anything other than that and they view it as weird.
But yeah, it makes no sense politcally. It's a double standard for sure.