The city guard makes the druid sign a paper stating that the animal (of which a clear description is given) is under his control and responsability, that he will take all necessary steps needed to ensure the animal will not put a citizen or his possession into harm, and that he will accept full judiciary responsability for any accident that may happen because of the animal.
Further, a special excise tax is paid for the animal, depending on its size.
Finally, the druid is given a list of places where the animal may be kept -- from zoo to inns with the necessary accomodations.
Remember that commonplace animals -- like horse, dogs, cats, etc. -- were accepted in medieval Europe, despite the fact that dogs or horses can be dangerous. They were assumed to be handled correctly. There's no reason this would not be the case with a druid's pet.