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?
If you go in the door you’re indoors but if you don’t you’re outdoor.
This could lead to a strange situation where you enter the cave through a doorless entrance and leave through an entrance with a door, making the outdoors indoors in the split second before you fade from existence.