That's a ridiculous example, and in fact it proves the opposite.
Notice that we only shoot bears that are actually eating hikers, even though no bear actually have moral responsibility toward us; that's because we as a society do feel moral responsibility towards bears (and animals in general), and therefore avoid shooting them except when required.
We certainly don't feel anywhere near the same moral responsibility towards animals as we do towards people, but we feel some. And as society becomes less religious, that'll tend to increase.