Nothing should be tax-exempt. In the grand scheme of things, if you want to make economics work, you have to accept that the reason we need government is for the bureaucracy to manage, protect or obtain the things people want/buy in civilization. The best way to do that is through sales taxes. They are anonymous. Exemptions for specific items (food, clothing, etc) can be handled at the purchase point.
Churches put the same demands on infrastructure that anyone else does, and they should be paying for that privilege. People should not be taxed for their production, only their consumption, and everyone should have to pay the same. The constitution says government can’t endorse any religion (or lack of). It doesn’t mean we shouldn’t tax them.
Good works? Why should anyone have to file for permission to get a tax exemption to be ‘favored’ by the government over other people? It’s just unnecessary bureaucracy that makes a certain type of criminal confidence game(selling a product that never has to be delivered) seem legitimate to an ignorant public that is bullied into believing in imaginary solutions to imaginary problems.