To me, the debate boils down to whether we are entitled to our own tax money (as in "it's already mine so don't tell me what to do with it"), or whether it's an essentially charitable social program that the gov't needs to manage as a fiduciary.

For schools, conservatives are annoyed their tax money goes to schools they consider worthless. Of course they'd prefer their money going someplace they consider valuable instead! I'm sure it could happen someday, but I don't see any religious schools seriously making an argument they should get more money than what the gov't already spends per student, only that they shouldn't be forced to pay for bad schools instead of good ones. And it's only a big issue because the public school system is demonstrably and massively screwed up, and a huge money pit.

On the SNAP program, my opinion is that it's a small issue (by comparison of course), but it's qualitatively different in that SNAP, rightly or wrongly, is seen as a program that is essentially charitable, and that it requires fiduciary oversight to make sure it isn't abused.