Is there any way that I can completely unbind an action from every button? In vanilla you hit ESC when selecting a keybind, but that button is already taken for canceling a controller button-bind.

I'm also looking for an answer because there's too much key in the binding menu for my controller, but I can't find any answer on the internet...

Sorry, it's not clear. You can right click instead of left clicking and it'll remove the binding. I'll make sure this is more clear in a future update.

I've make this more clear in newer versions of Controllable with a tooltip.