I think they should definitely pay taxes. Or at least ones that make a certain % more than their overhead costs, like land, electricity etc.
Edit: Because this was mostly me asking the flood, I decided to research it more.
This is the best info I have I found
http://churchesandtaxes.procon.org/
So my final conclusion is that if religious institutions were paying taxes it would cause a breach in the separation of church and state, and it would create a large conflict of interest. So at this juncture it seems things are better left as is.
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I can't speak for every church, but the people who attend them tend to be extremely charitable to begin with, and lots of them are involved in community services already. You'd be stunting that and forcing the money through inefficient government programs.