I have been astounded by the behavior of some people with regard to pets. You might care deeply about Fluffy, but all it is a animal. An animal that you care about, sure, but taking care of citizen's pets is not, to my mind, a useful or appropriate function of government.
When we've had pets, sure, we liked 'em and cared for them, but I ain't bringing an animal with me if I have to evacuate, and I sure as hell don't expect my tax dollars going to take care of them.
To my mind, the only useful thing that government can or should do about pets left behind after a natural disaster is to kill the ones that are nuisances.