Of course it’d be pretty horrific to see a stuffed deer head mounted on the wall – amongst a group of anthro deer especially, but amongst ANY anthro character too, I’d imagine.
But of course it all depends. Whenever we consider such things in an anthro universe, it inevitably comes back to this question of which creatures are “people” and which ones are “actually” animals. Feral versus anthro, I suppose.
My favorite example of this is: consider how the wildebeest in The Lion King aren’t people – they are just a mindless herd of animals into which Mufasa falls and then he’s stampeded to death.
I don’t really have a point here. I just wanted to share a thought that I had while writing my story, which is a setting where birds and fish are NOT anthro, and that’s why it’s “okay” for the seafood restaurant to have a giant swordfish mounted on the wall.
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.