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.