Louis "Is it fair that Pluto has to wear a leash and sleep in a doghouse while Goofy, who is also a dog, gets to drive around in a car and play golf with Mickey?"
The various Muppet productions have had some fun lampshading and subverting this issue. To wit:
On The Muppet Show, Gonzo, an anthropomorphic... birdlike... something eventually revealed to be chicken hawk, and was thus dubbed the set's resident expert on chickens, seemed to be in a relationship with Camilla, a non-anthropomorphic chicken who only speaks through clucks.
And there have been both talking puppet chickens ("I'm a chicken; this sketch is a turkey!") and ordinary chickens on the show. If he wanted to dance with a chicken... well... but then, getting a puppet chicken that could actually dance would've ruined the comedy of watching Gonzo urge a real chicken to "please do something!" would have been compromised.
Gonzo once tried to romance a cow. And not a Muppet cow, either. A real cow.
In one segment, Rowlf, a Muppet dog, sang "What a Wonderful World" to a non-Muppet dog. This could be excused out of sheer adorable.
In The Muppets Take Manhattan, Kermit (with temporary amnesia) goes into hysterics at the thought of a Frog wanting to marry a Pig, complete with ridiculous puns. Did amnesia turn him off the idea of Interspecies Romance? And in one episode of the show, an android Kermit replica — long story — flirts with Piggy thusly: "A frog and a pig! We could be married and have bouncing baby figs!"
A Muppet Family Christmas ended with Kermit giving Miss Piggy a gift of a mink — a live, anthropomorphic mink who proclaims herself Piggy's biggest fan. Creepy...
Maybe the Muppetised, singing fruit was a parody of this? ?Momma always told me, never eat singing food.?
By far the worst was the Denny's commercial, with Piggy happily ordering meals the included ham, bacon, and sausage.
Not to mention the original plot of The Muppet Movie, in which Kermit refuses to advertise frog legs because he is a frog, and would not want to contribute to the slaughter and consumption of his own species. Except ... he is a singing, dancing frog who talks and acts like a human, and has way longer legs than the frog legs advertised.
Played with in this Sesame Street sketch. Kermit's reaction when the frog is brought out says it all.
Two web shorts involve the skateboarding dog. The Muppets, including Rowlf, seem completely unable to distinguish between a real dog and a muppet dog, talking about him as if he were capable of anything a muppet dog could do.
In Dinosaurs, all the animals act like humans. Therefore, in a perfectly logistic twist and the natural solution for this trope, all the Neanderthal humans take over the roles of animals, acting or being treated something like dogs.
Shows where the characters are portrayed as people in costumes may get a bit more slack with this trope. Nonetheless, there are a few episodes of Zoobilee Zoo that are thought provoking:
In one episode, Lookout Bear adopts a non-anthropomorphic dog played by a real dog. The image of a guy in a bear costume playing with a real dog was pretty jarring. (And we'd give anything within reason to know what the dog was thinking.)
In another episode, a witch arrives to bully the residents of Zoobilee Zoo by making them — and these were her exact words — "act like animals!"
Finally, there was an episode where the characters travel back to Zoobilee Zoo's distant past and meet a human caveman. (Really, the only way all of this could make sense is if the show takes place at an Anthro-Con that never ends.)