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 think no because a lot of churches (like mine) are very low funded and are funded by donations. Also many churches (also like mine) help out the community immensely by hosting fundraisers, renting out community halls and volunteering