It depends on if they're a character or not, whether or not it bothers me.
Say with Ray's opening, whatever animal is being hunted isn't a character to me, so it makes no nevermind to me if they get killed.
If the animal is a character, has a presence and a personality, then their death will hurt as much as if a favored human character dies--but it can be worse if that death is a sacrifice or not. Animals are sentient, but they're no more intelligent than children. It's not a matter of purity to me, it's the fact that I don't believe they can make a thought-out decision whether or not to sacrifice themselves or not. I don't believe that a healthy dog, for instance, can conceptualize that throwing himself in the way of that bus could get them killed because, I believe, healthy animals don't think about their own death the way we humans can. I just don't see that animals can make those choices that I take for granted as a person.
Thus, when an author has the animal doing something fatal that, for a human, would be heroic, I find it out of character for a real life animal, thus making it a cheap and obvious emotional-button pushing authorial device. Ruins the story for me on so many emotional levels that I refuse to knowingly do it.
All this doesn't apply if, for whatever reason, it's proven that the animal IS capable of making human-like decisions (Dean Koontz's Watchers comes to mind).
But that's why I won't read stories where an animal or child gets sacrificed heroically--they couldn't've made the decision, so it's a fake heroism.