Well, I tried this addon in my server on LAN game mode (maybe I'll investigate both the internet connection and the singleplayer modes), and absolutely nothing works for me (in terms of climbing, wall jumping, and ledge grabbing). I've looked at all of the comments on this thread and tried everything, but none of it works. I also checked my console; the addon was loaded in perfectly fine, and I received no errors during my test. I will go ahead and try to disable all but default addons and if it works, try to pin a certain addon that breaks it.
EDIT: So I just tried it with only the default addons and the parkour player addon enabled. It still did not work, so as far as I know there is not an addon that breaks this.