If you can't afford your own transportation for your family AND your pets, you got no business owning pets and imposing the cost/burden on society for the rescue of same. Sorry if this seems heartless. A dog takes as much room in a shelter or a chopper as a child.
I suspect you're going to lose this argument. The legislation says the funding is contingent upon state and local governments working these arrangements out. That means planning.
You are not going to dictate to people whether they can or cannot own pets, and governments are going to have to figure out how to deal with this situation.
Besides, nobody said anything about putting animals in shelters for people. The Baton Rouge shelter accepts people with pets, but hands them off to the Louisiana SPCA, where they are cared for.
Why can somebody take a big bag of mementoes, but a little kid can't take a kitten?
Well because the mementoes don't run all over the place, require feeding and make messes. And as a practical matter I do not think you are allowed to take whatever you want with you if you are evacuated by the government or are given housing in a shelter.
I say all this as someone that has owned dogs my entire life. I know that if I were evacuating my family, we would take our dog with us and I suspect if we had to be evacuated, my family would go and I would be staying with her. But these evacuations only happen in crisis situations and to require, as a condition for federal funding, that all these local agencies care for pets in the midst of a crisis without regard to the realities of the situation strikes me as some ridiculous grandstanding.