I’d say it depends. So long as the religion in question follows all the proper rules related to non-profits, they should have the same tax benefits as other non-profits, including tax exempt status. However, I agree that religions shouldn’t get any extra benefits that aren’t afforded to other, secular non-profits.
Well, I’m not a tax attorney or accountant, but I believe for any non-profit to have tax exempt status, it needs to be apolitical. I remember a while back when donating money to the ACLU, they said that I couldn’t claim it as a tax deduction because it was a political organization, despite also being a non-profit.