Being treated from tax perspective the same way as every other legal entity without extraordinary privilege is “breaking separation of church and state”?
You might be interested in reading Walz vs New York [1] for some background on this subject. As with most things, it's nuanced, but you essentially have two choices here: tax the churches or don't. Most have agreed that the former has a much greater risk of violating separation of church vs state (excessive government entanglement) than the latter. You're free to disagree, of course.
[1]: https://supreme.justia.com/cases/federal/us/397/664/