I pay income tax, does that mean I don't freely exercise any of my rights?
Taxing a church property isn't in any way prohibiting a religion from existing.
In the context most relevant to us and reading the new testament you don't even get the impression Jesus had in mind the kind of 'church' as we now think of it.
Yes. Yes, when you pay taxes, you are giving up some portion of your property, property you’d otherwise be free to enjoy as you please, in order make that payment to the government. Taxation is theft. It (especially income/payroll taxes) can only be collected via forced collection through the implied threat of loss of liberty. They are especially repugnant to exercising your right to pursue happiness...you cannot avoid them.
Playing games about who pays how much and who gets special exemptions and privileges is really just arguing over where the deck chairs go on the Titantic.