Is the wall jump allowed in any%. It's not stated as illegal in the rules but no one seems to use it.

Anything you can do within the run without modifying the game should be allowed. I'm not sure what wall jump you're talking about. If it'll save you time, use it.

To clarify, wall jump is the ability you gain in the hidden challenge box you can find on level 1, it probably saves up to 2 seconds if you start the run with this abiliy. It doesn't save time in any% but it's enough to introduce an Any% NG+ Category