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.
Can’t answer for @BlubberSeal, but in my hand-waved sci-fi setting, I’ve gone with a two-part solution for pets.
Feral animals are genetically and socially far enough removed from anthros to be considered their own primitive species. They are treated like in our world.
Pets are inconvenient in a high-tech space future, so if anything, most people have robot pets designed as small feral animals. These double as ‘intelligent’ personal technological interfaces (think smartphones, but cool).