I’m not sure what you mean about religious groups’ aid being secular. It seems like you are saying medicine and food are “secular” things, while prayer is a “religious” thing. Sure you can’t pray money into existence, so it’s sort of a “secular thing”, but the useful question is really who is giving the thing, not how it came to be.
The issue at hand is what organization is at the source of the charitable donations—a secular organization or a religious one. That’s a question that is worth asking. Whether or not the aid they are giving has been originally created by a god, magic or science isn’t really important for this question.
I didn’t downvote you, but I suspect whoever did shared this reasoning.
What about the policy of making an effort on your own and opting out of groups of either variety?