Eh, gonna play devils advocate and defend PETA here. Fair enough, nothing says Mario brutally kills Tanooki Racoons and wear their skin (it's actually MORE plausable in this game that "a wizard did it". It's a Mario-game, ffs. He's a fat italian plummer with a pedostasch that dating a princess, it's already unrealistic enough as it is), but what PETA is trying to point out is that Fur Is Murder. And while Mario Doesn't Wear Fur, they probably won't to point out that people IRL do kill these Tanooki-racoons for their fur, and that by Marios association, these furs IRL might be more socially acceptable. Or some similar logic.
PETA might be severely retarded, but breeding animals in small, tight cages to wear their skin isn't very ethical (in my mind) either.