The animals are well behaved and it's no big deal.
Frankly, I wish my tenants got cats. I'd much rather have cats than hear them whine about mice. I love my cats as family, but I would get one anyway to keep the mice out in the winter.
Just get them to pay a pet deposit and be done with it. People love their pets and it's cruel to keep the separated. I would not live somewhere without my cats.