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Fair, so donate time. And pitiful you feel the way you do re: religion charities. Some do tremendous work. You just need to find the right ones, like any charity.
I do donate time or physical items that are not cash. I'm the past I also worked with a veteran's group who placed homeless vets in housing. I had a 4 unit apartment building that was all section 8, and when a unit became available, I would let them know first. This wasn't truly charity in that I was still being paid, but I was making housing available to people who normally would not qualify for it. I no longer own that building or section 8 rentals, but I would do it again if I did.
Some Religious organizations may do good work, but I have neither the time nor patience to weed or and sort through them all to find the ones who aren't bigots. After that, I have trouble giving money to people who are justifying their actions as a way to please the adult version of Santa Claus. (He knows if you been bad or good, he'll bring you gifts if you ask nicely and be good, if you've been bad you get coal). It feels like I'm enabling the delusion.