If you tax non profits like any other business they would either have zero to pay in taxes or they would only be paying taxes on whatever savings they have.
What's the problem?
If by taxing savings you mean investment earnings on assets then sure, but otherwise what you're doing is taking taxes in surplus years without the expectation of getting that back in deficit years.
Example (at 20% tax rates, mega simplified):
Year 1: Revenue: $20; Expenses: $10; Tax: $2
Year 2: Revenue: $10; Expenses: $20; Tax: $0
This organization, over two years, has made no money yet has paid taxes. The theory behind not for profits makes sense and should apply to religions.
Where I disagree with current law is the exemption from property taxes, which doesn't follow the same theory, and also tax deduction for donations.
The portion of religious donations that go to legitimate charitable activities should be deductible, but otherwise I see no reason why donations to run weekly prayer gatherings should be deductible but dues for any other social club is not.