I have been playing around with this bug and most people say that it is tied to the frame rate, but from my experience i have been able to undo the cannot move state from a character by canceling out the fight menu and walking around before the end of combat. What seems to be happening is that the combat state is staying on and trying to execute combat commands with no target causing all other non-combat controls to not work as if Move in Combat was turned off, this is tangentially tied to the frame rate because in old games processing speed = frame rate but it seems to not be the actual problem, a quick solution could be the end combat state needs to run/activate a few more frames or times when combat ends. If i am right, someone could easily turn this into a Workshop mod where the end combat command is added, also this seems to a/effect melee characters more.

More support for my theory is that upon reloading a save your able to move, and that is because loading a save wipes almost all states that toons are in.