I do think that Spiegelmann is still dealing in human and animal stereotypes, although he goes about it differently (and inconsistently - it depends on the animal). The vermin one is the Nazi stereotype of Jews (and that's the most interesting one). Frogs is a worldwide association with French cuisine, plus his own assessment of French people's un-sweetness. Gypsy moths are... word association. The Swedish reindeer appear to be regional association. The pig one I'm not sure, because the wiki page is a little vague. I mean, it's very hard not to deal in stereotypes of some kind if you're going to make an allegorical shortcut that people will immediately "get."

I don't know why he chose cats or dogs, although I would guess he was going for the traditional Tom and Jerry motif (mice are the sympathetic protagonists, cats are evil, dogs are allies of mice) that Western audiences are familiar with. And yeah, this is the one I dislike the most.

Granted, that doesn't take into account his quote about wanting the metaphors to self-destruct. Maybe they do; I don't know. It's hard for me to imagine how they could, but I've been wrong before. I think that classifying Jews as vermin (but in a positive light) is definitely lampooning and destroying a Nazi metaphor, but as for the other animals/characters, I don't see it. It feels more like replacing Nazi animal-human metaphors with his own.