-Not really punk, but Pepper Coyote does a lot of indie. Songs like “When I Die” are really good.
-Niic, not punk, but very techno-pop. Also, almost all of his songs are about furries.
-Solence, not furries, but songs like “Animal in Me” fit what you’re looking for.
I hope this helps a bit. I had a furry playlist a few years ago, and this was some of the stuff that was on it.