You’re indoors in the sense that you’re protected from the weather and the elements, and the cave could even have some kind of covering or entrance area that could be considered a door or doorway. People have built homes in caves.
Is caving an outside, inside activity?
Caves are outdoors because a bunker is indoors and the cave around it is outdoors.
Just for the sake of argument and fun:
Aren’t we all outdoors because we are living in buildings that are themselves outside?