I'd be fine removing tax exemptions for all of them.   At the very least they should be paying for basic services received from their city.   I'm honestly not sure how far the tax-exemptions reach.

As you point out, the rational is probably based on the Church  being addressed matching the goal of the dominant party.

I'm opposed to the mixing of church and state, primarily because it deeply damages what I see are the objectives of Christian teaching.    The  teachings of Jesus and the early followers have been corrupted by the Church and it's thousand years of political rule.    

Those who internalize their faith are completely secure that it can never be taken from them.    It's only the insecure that need others to reinforce their personal belief system.     I've never been  stopped from praying, not in my home, not on a baseball mound, not in any of my schools, both private and public.