"Although I do wonder if the fear of reprisals (or actual pressure at the time to do so) would make me save the stranger instead, although I'd never forgive myself for leaving my cats to suffer."
I think this is where a lot of the logic, including Singer's, goes out of the window. In my experience, at times of crisis people work on autopilot, they don't think through concepts such as 'will society condemn me for saving my dog over a stranger' - there simply isn't time apart from anything else. Instinct takes over, and I believe my instinct would make me go for my dog.
However, and this is another important point: we can't know if our hypothetical stranger is a rapist, murderer etc. or an exemplary human being, but equally our hypothetical rescuer cannot know in advance that they only have the chance to rescue one of their two options. I would go for my dog fully intending to go back in afterwards for the stranger. We know that won't be possible, but at the time of the hypothetical event, the characters don't know that.
I have no interest in trying to justify my instinct, it is my prerogative to choose my dog, but I know part of my reason is the lack of free will. As someone else pointed out earlier, he didn't choose me, I took responsibility for him. He'd been abused and I promised him he'd never again have to feel hunger, fear, pain, insecurity etc. and that I would always look after him. It was the most solemn promise of my life and I'm proud to say I've done it.
There would be a physical pull between he and me in that fire - he feels fear, pain, jealousy, love. He sulks when he doesn't get his own way, he looks to me to fix it when he is in pain. Who is to say he's less deserving than a human being? I cannot quantify the love and devotion he's given me - and he's been doing it longer than my husband and more consistently than any other human being I've ever known. He's never hurt me or made me doubt myself, or any of the other things even decent human beings do to each other.
Furthermore I always feel humans are more capable of understanding a situation - if my dog is in that building, it's because I put him there. That's not likely to be the case with the human, therefore he/she is not where my responsibility lies. The idea of him being stuck in that fire, not understanding what's happening and wondering why I haven't come to him makes me physically clench up. I couldn't leave him. We've been through a lot and I owe him as much as he owes me. Just a dog? No way.
Sorry, that was really long!