Well, they manage it poorly if cases like Storm are any common
as far as shapeshifters, i think only the greek gods have been mentioned. my question would be if the labyrinth forcing mythicals in their true form would have any effect on a werewolf like being, or if shapeshifting abilities are merely misinterpretations from people who are unaware of the existence charms.
It's an interesting question... The hotel has only disabled the illusions while maintaining Asterion's physical changes, so shapeshifters could theoretically still disguise themselves, but it's entirely possible that it only happens because of his role as the "Prisoner" and everyone else is forced to their true form, though that raises the question of what the true form of a werewolf is
If we're talking about the same explanation, then that was in terms of "shapeshifting is a physical change, passports are a perception change" distinction.
Which would imply that, in reference to the "true form if they enter the hotel" question below, that a werewolf would still be able to shift, because the passports that the hotel 'turns off' doesn't effect any material changes.