I just don't see why any church gets a tax break unless they comply with the same charitable rules (mostly non-discrimination) that everyone else uses to get tax breaks. I'd like to avoid paying my property taxes by inviting a select group of friends over for dinner once a week and calling it a community benefit, but I doubt the assessor would agree to it. And even if I did manage that, eventually all the neighborhood dinner parties would be hard to get to with the roads falling apart.
Treating churches whose doctrines are politically acceptable differently from those whose doctrines aren't amounts to preferential treatment. Most Muslims don't have a choice about maintaining separate worship facilities for men and women; for them that's part of being Muslim. Tax them for it and you have what amounts to a tax on religious doctrine, which is constitutionally unacceptable.
Nonprofits aren't necessarily charities. Churches and political parties also qualify. Should the party in power have the authority to tax a rival out of existence? Hands off is the only equitable approach, even if it means that newly-paved parking lot it took five years of bake sales to pay for doesn't wind up on the tax rolls.