The last time we were there, some whackadoo with little experience climbing
and the wrong equipment decided he was a mountaineer and started up a pinnacle. He ran out of steam on the way up and had to be rescued.
It was interesting to watch.
I believe climbing is, or was, allowed, of course with the proper permit, equipment and level of skill.
It's a gorgeous, gorgeous place to walk around. There's something "otherworldly"about it.