Web-based pet sims often have this problem. For example, carnivorous Neopets can and do eat other Neopets (a specific example is the abandon with which lupes eat chias), despite all of them being sentient. Like Pokémon, there used to be "normal" animals such as fish and cows to give milk but, except for some outdated materials such as items of encyclopedia pages, this practice is being phased out.
Beyond Good & Evil has anthropomorphic pigs, cows, and goats, among others...and a freezer area full of rotting beef. And a place called the Slaughterhouse. And Pey'j, a pig, seems to be the subject of several jokes about being eaten.
Pey'j: Thanks, Jade...if it weren't for you, I would've ended up on a plate with an apple in my mouth! Jade: Cut it out. You're making me hungry!
Since you handily collect species information about every animal in the game, it's worth noting that Pey'j is "Sus sapiens" (wise pig), parallel to "Homo sapiens" (wise man). So it's reasonable to guess that regular animals and their anthropomorphic analogs are completely different species and that it's fine to eat the non-intelligent kinds.
There's also an anthropomorphic shark who brags about his ability to devour "a family of five" in record time, along with his family's achievements in this area. A family of five what is never addressed.
In the Super Mario Bros. series, the Mushroom Kingdom is mainly inhabited by anthropomorphic mushrooms like Toad. Then in the Paper Mario games, it's discovered that normal mushrooms are also the Mushroom Kingdom's main food source! And there's also a pig who runs a hot dog stand...
Remember that this is the Paper Mario series, so it's probably deliberate.
Mario is friends with Toad, stomps Goombas, and eats big mushrooms and 1up's. Although it's never explicitly stated they're mushrooms; the Super Mario Brothers Super Show depicted them as midgets with no noses and mushroom hats. If this is true to the series, then the residents of the Bean Bean kingdom aren't beans who eat beans, they're green people who love eating beans. It makes sense that they're humans when you consider Peach is a human, as well as the fact that her Grand Mother was a Toad in SMRPG.
Of course there's still the question of why all the mushrooms have eyes...
Spore averts this — as a Carnivore or Omnivore creature, you can socialize with the same creatures you are capable of killing and eating. The same holds true in the Tribal stage, and any other tribes don't seem to mind if you're slaughtering other sapient creatures and consuming them. (Not averted so much if you're playing Tribal as a straight carnivore and offer a gift basket of meat to a tribe of herbivores...)
Animal Crossing, being Animal Crossing, mostly avoids this. Characters are pesco-lacto-vegetarians.
Well, AC avoids this for 364 days of the year. The most obvious exception is the "Harvest Festival", wherein everyone in town gathers at the wishing well for a great big Thanksgiving-esque dinner with no turkey. The only food there seems to be stuffing, vegetables, and the like...with the exception of one big, empty platter. As it turns out, the "guest of honor", a turkey named Franklin, has been in hiding ever since he got a letter from the mayor.
Franklin: "We cordially invite you to be the main guest at our annual Harvest Festival. Heh heh heh hoorf..." What's wrong with that?!? I can even see where the word "dish" was erased and then replaced with "guest!"
While Franklin is never actually eaten (it's Animal Crossing, after all,) the implications of the whole thing make this the grade-A, prime-cut stuff of nightmares .
In City Folk, at least, the villagers seem to genuinely want to welcome Franklin; they'll say something that sounds bad, such as 'I can't wait for dinner with our guest', then follow it up with 'I even researched his culture's food and made some so he'll feel more at home'. Mayor Tortimer is really the only one being truly creepy about it.
The rest of the year, there are several different foods available for the villagers to discuss in their mix-'n'-match randomized dialogue, and the game goes to very careful extents to make sure to specify that every food that could possibly contain meat is either a "vegetarian" version or made with fish. Examples include salmon ravioli and vegetarian meatloaf. At least, in Wild World and City Folk. The first game wasn't so careful. Giant cow talking about hamburgers, anyone?
Occasionally, an animal villager will ask the player character to catch a specific fish, not all of which are biologically fish in the modern sense. But two species of "fish" in the game are the frog and the octopus, and some of the villagers are frogs and octopodes.
In the casual Hidden Object GameMushroom Age the first era you travel to is Dinosaur Age, where you meet a T-rex. He has a toothache, and the game character explains that it's from eating meat and that he should only eat fruits and vegetables. The puzzle following is sorting the things he "should" eat from the things he "shouldn't".
Banjo-Kazooie isn't subject to only carnivore confusion, as everything, from the eggs used as ammunition to the orange given to a hungry monkey, is alive, sapient, and capable of Speaking Simlish. Making it worse/better is that most of them are rather accepting of their fate; for example a fish that can be rescued in the second game that isn't even mildly annoyed it was about to be cooked and eaten before the plot arrived.
Made worse by the fact it was canonically his pet goldfish.
High up on a cliff in Metal Gear Solid 3: Snake Eater, if you kill a guard, buzzards may feed on his corpse. If you then kill the buzzard and collect its meat, you get a bigger dose of stamina from consuming it.
This comes back to haunt you when facing The Sorrow, as the spirits of all the people you killed up to that point march along the river towards you. If you ate the meat of a a buzzard that scavenged off a guard, he'll come shuffling towards you, crying "You ate me!"
Brought up by Arcueid Brunestad in Tsukihime. When asked by the main character why she, a vampire, didn't eat humans, she asks him if he would eat animals if they could talk to him. The interesting thing about Arcueid is she's been Raised by Wolves so came up with this value by herself.
Furcadia makes it clear that the major non-sentient lifeforms in the planet suitable for food are fish and birds, yet there is a playable sentient bird-race...
The classic Ritman/Drummond graphic adventure Head Over Heels, as well as being one of the cutest games ever (check out the remake on RetroSpec), has save points in the form of Reincarnation Fish which "like to be eaten ? there have been reports of them jumping onto plates".
The game Lugaru has wolves and rabbits, both heavily anthropomorphised. In the game, the wolves state their desire to enslave and eat the rabbits on the island of Lugaru; for some time, apparently, the wolves and rabbits lived in balance, but in the game the rabbit king turns traitor to the wolves in the attempt to save himself and his family, forcing the main character (a rabbit) to kill all the wolves.
Played straight in Abe's Odyssey (and its sequels). The glukkons want to use their cheap labor as a cheaper filler for their new taste sensation.
A short instance in Terranigma finds your character, Ark, trapped in an icy cave with a talking goat. . . and the goat's dead husband. The next morning the goat asks if you are hungry and would like some breakfast, before walking over to her husband (complete with dramatic music cue).
The goat claims they must do what they need to survive, and the world would be without another goat otherwise. Ark becomes distraught and decides against the offer, disgusted. The goat informs him that he, "must be stronger". Shortly thereafter. . . the goat opens up a new area by ramming into it, and the character can climb to safety, the goat informs him she will make it out later. She doesn't. If you go back to the same area later, you will find not one, but two dead goats. She cannibalized her husband for nothing
Periodically shows up in Touhou. Mystia Lorelei the sparrow youkai is frequently subjected to poultry jokes, starting from her debut in Imperishable Night, where both Yuyuko and Remilia apparently feed on her in their respective storylines. In side material, Mystia is sometimes seen shilling grilled lamprey as an alternative to poultry.
At the summer festival, if dating Ryouta, they go to a yakitori stand for dinner. Afterwards, Ryouta provides a possible Hand Wave by commenting on the differing rates at which different birds are becoming intelligent.
Given a dark twist if you date Dr. Iwamine, who murders Yuuya and sends the heroine his roasted body as a Christmas feast.
Yuuya's route has a mention of the rumors about the poultry in the cafeteria and the quill pens sold in the store. Turns out some of both are made from the bodies of students who have disappeared.
In Etrian Odyssey IV: Legends of the Titan, you can hunt at various points while flying to get food that gives you buffs. In the third area of the game, the food you get from hunting spots is rabbit meat. After completing the third area, you unlock the Bushi class, who are antropomorphic animals, including a rabbit as a possible choice.