If I enter a dungeon or cave manually, via my own discovery, early in the game... Does that permanently disable it to qualify for a Radiant quest later on? Or does the dungeon respawn for new quests somewhere down the line?

No, it doesn't remove it from the list of potential targets. This actually leads to some issues with dungeons that don't reset but are radiant targets like Broken Oar Grotto, where you get the dungeon as a target but the objective doesn't spawn because the dungeon hasn't reset.

Thanks for the answer. Usually I would say the above svcks, but for now, I'm glad. I wanted to do some minor exploring early on, but not ruin quests. Glad I won't.