Furry Writing, Worldbuilding, and Storytime

I know it's not the most elegant solution (it's practically the goofy/pluto dichotomy), but in my story, anthro animals and feral animals are a completely different species.

Every animals has two variants, anthros and ferals. Both are completely different species, and the anthros treat ferals like we treat animals. With that, it's not weird for anthros to hang feral heads, though anthro deer hanging a head of a feral deer would be a little jarring, like humans hanging the head of a monkey.

To be fair I usually take a more handwaved approach to worldbuilding. I focus my story more on its moral value as opposed to its worldbuilding. It doesn't help that the few stories I write right now are about either a single anthro in a world of humans, so anthro worldbuilding are nearly nonexistent, or a simple and straightforward aesop-like story with very few worldbuilding.

In a sci-fi/fantasy game I never finished writing, there's a privatized police force that taxidermies their prisoners and showcases them in a museum.

It's an interesting concept to explore. Certainly, it would probably be macabre for an anthro deer to see a deer mount on the wall, akin to visiting Buffalo Bill's house in Silence of the Lambs and seeing his sewing room. Real life analogues do exist though. David Sedaris, the famed humorist, once wrote about trying to acquire a real human anatomy skeleton he found at a shop in France for his husband. That guy who died at Mammoth Cave in Kentucky was kept in a glass coffin for viewing (for a fee), as was Lenin's body. I once personally encountered a shop in Hampden which centered itself upon the sale of the macabre, and while I don't believe they were for sale (I honestly didn't think to ask), did have several (allegedly) real human skulls on display in amongst the antique surgical tools and vintage taxidermy.

At its core, its the "Goofy/Pluto" dichotomy. It's Mae in Night in the Woods seeing a fat raccoon in the center of town, when she herself is a bipedal talking cat and bipedal talking raccoon characters exist in universe. I think it's hard (if not impossible) to really fully imagine the mechanics of how an anthro world would be constructed from our vantage point as humans. Despite the fact that, at our core, we're just smarter apes, we've so removed ourselves from the natural world that there's us ("people," who are intelligent, reasoning, and thinking...allegedly), and then there's "animals," which is every other living creature on the planet over which we hold dominion. Trying to create similar structures and analogues is hard because of how/where to draw the line. To us as "people" it seems rather clear. To us as imagined "animal-people," it's much more difficult.

In my opinion, it's also difficult to create settings that feel "alive" (for lack of a better term) without wildlife of some sort. I went the same direction you did with a story I wrote once where birds, fish, amphibians, ect. were a natural part of the environment as "animals," and then most mammals (like canids, felidae, cervidae, mustelids, whatever possums are, ect.) were "animal-people." In my head, those rules made sense based upon the relationship between those two "classes" (for lack of a better term) of animals, so that fish and birds could be guilt-free food and I could populate creeks and streams with crayfish, salamanders, ect to give some texture to my rural setting. I also felt like it was easier to write about critters with paws which could be used in an analogous manner to hands and with biologies similar to ours.

An example that went the complete opposite direction would be Bojack Horseman, with critters of every kind being anthropomorphized in that show. It played with that concept to great comedic effect and handwaved the rest, which worked perfectly for the setting the show had created (at least in my opinion).

I think either way works as long as there is some sort of framework or rules that doesn't trip the "Goofy/Pluto" dichotomy. That's my $0.02 worth.

For most stories, I think handwaving or lampshading the weirdness of it is the way to go.

For the remainder... I'd say it's a matter of what kind of culture you want to create. Taxidermy is one of the problematic areas, but there are many more, such as, but not limited to: pets, cattle, wild animals, and food.

Food is probably the easier to step into. Is every anthro herbivore? That may work if you have an herbivore-only world, but may become jarring if you have carnivores too. If you accept that you need meat, and you aren't willing to handwave it away, where does it come from? The way I see it, as soon as you have meat, you need wild animals to provide it.

Wild animals then. In some settings you can dodge the problem. On magical settings, you can have anthros being sentient, and magic creatures not sentient, and that's where the meat comes from. On sci-fi settings you can dodge it with all wild animals beings extinct, and meat being synthetically created from some of them. On more "normal" settings you can maybe have only one sentient species, and every other being wild/non-anthro, or maybe only mammals being sentient, and all others being wild (Imperium Lupi goes with this. Wolves, and hyenas are the main species; bunnies, pigs, + others are "secondary" species; bugs and fish are all wild + magic (iirc)). If you have an all mixed setting... you're kinda screwed. You're gonna need a whole lot of either worldbuilding or handwaving.

As a less hypothetical example, in my ongoing Star Fox fanfic I mention synthetic meat, and rely on the "readers only make level-1 questions" assumption to avoid going deeper into that particular rabbit hole. If it does turn out to be necessary, however, I can always handwave it with "alien wild animals". Things such as pets, though? I won't be touching that subject with a 10-foot pole, there will be exactly zero mentions of any domestic animals, it is not worth the trouble.