The tax deduction for donating to churches (added to the fact that churches themselves don’t pay taxes on their income) isn’t based on the idea that churches do all that much in terms of charity. The reason it’s there is because 1) churches are good at mobilizing voters (especially for Republicans) so they expect a kick-back, and 2) certain politicians (especially Democrats) are deathly afraid of being seen as anti-religion. So I don’t see this changing for at least a few decades.
Ed Dolan has a post about the charitable deduction, 35% of which goes to religion. Of that, only 17% goes to “missions and ministries,” which, frankly, isn’t all charity either. It’s charity-plus-proselytizing (read: enlisting future volunteers and donors), sometimes even charity-after-proselytizing. So maybe we can be generous and say that only half of that 17% is actually charitable?
All to say, of course, that anyone who thinks that the government is “anti-religion” with all this government money being dumped into religion isn’t living in the same universe as the rest of us are.