He said it about dogs. That doesn’t equate to a papal dispensation for cats, let alone disease germs :-).
Actually, following the creation account, certain animals are referred to with the same term, nephesh, that refers to human souls elsewhere in the bible. These tend to be the more intelligent animals, the ones that have a degree of what we would call anthropomorphism.
I’m one of those horrible Protestants, I don’t require the pope to tell me dogs have souls.