What ability set would be bad IRL?

[Troacctid]

Being a Cleric, Paladin, or Divine Soul Sorcerer mostly. Even if someone looks at your Divine Intervention abilities and says that they're "just weird spells", they would have a much harder time if one of the spells you cast is Commune and you can reliably talk to God 5 times per day. To say nothing of what would happen if you were a Cleric of one deity and you met another Cleric who could similarly demonstrate that they were in contact with a different deity, immediately disproving monotheism.

All that proves is that you personally believe your magic is granted by a deity. It doesn't prove the deity's existence. You say you talked to a deity? Cool, get in line behind every prophet in history. You have miracles to back it up? That just proves the existence of magic, not the existence of Mystra. And miracles can be faked, so it might not even prove the existence of magic!

Other spells like Contact Other Plane or Planeshift would have a similar effect on any religion whose creation story says that there is only one 'Earth' with sentient life upon it.

Again, that doesn't really prove anything except that you believe you talked to, or traveled to, another plane of existence. Open a planar portal in a major metropolitan area and then maybe we can talk.