I included kittens in my post to be a no-no as well as puppies. I've never seen it where I live but I would include pygmy goat, potbelly pigs, primates etc. to my no-no list.
I might start a YT War but here I go....
Mice, Rats, Rabbits, Ferrets, Hedgehogs, Chinchillas, Guinnea Pigs, Hamsters, Birds, Fish & Reptiles, etc. for me, seems to be ok since these are types of animals that requires to be confined for their safety. I can't imagine allowing any of the above to have free run of a house. I do get really upset and have spoken to various store managers if I see several dead fish in one tank. I've never seen anything else deceased in pet stores (unless you count crickets!)
I know I'm gonna hear it from the Rabbit, Farret & Iguana people so I'm bracing myself!