That’s certain to be one of your fallacies, changing the emphasis and meaning of the term ‘respecting.’ You’ll have to look up which one.
It’s well known that the Court has been wrong in numerous of its rulings. But historically, from the beginning of this country, the government has contributed to religious establishments without establishing a State Religion. And the Court has rarely found it to be in violation of the Constitution. The one that allows freedom of religion, not seclusion from religion. By your implications, NGOs and non-profits (that don’t pay taxes) would be excluded for the off chance they would benefit a particular group, when that is often the goal. The situation has simply never been as you describe.