We have a law in Texas that an Atheist can't hold office. Really stupid, but it would have to be challenged to get rid of it.
edit: went and looked it up
Article 1, Section 4 of the Texas Constitution states, "No religious test shall ever be required as a qualification to any office, or public trust, in this State; nor shall anyone be excluded from holding office on account of his religious sentiments, provided he acknowledge the existence of a Supreme Being."
Yes, it's unconstitutional....buuut, the shitty way our political system works, somebody would have to sue to get it removed in Texas. Until someone does, they're going to enforce it.
The text is never going to be removed for sure because that takes action. But also no one is enforcing it either. I'd love to hear about anyone it's been enforced against, if they exist.
I just asked who has been barred from the ballot as a result. I'm aware of Republican candidates raising the issue in TX, only to be informed that it's unconstitutional. To my knowledge, no one has ever been barred since that case. If you have different information please let me know.
If someone were barred, they would sue in federal district court and immediately receive an injunction. Federal courts cannot ignore precedent from SCOTUS.