What’s your favorite non-anthropomorphic cartoon animal? Mine would have to be either Tom or Jerry.
Gromit
Yakky Doodle
I’ll assume that by “non-anthropomorphic,” you mean they don’t talk. In that case, I’ll go with Gromit too, followed by Snoopy (in the funnies).
Otherwise, Rocky and Bullwinkle come to mind. So does Brian Griffin.
The Road Runner and The Coyote.
ETA: There were a few times the Coyote addressed the viewing audience. Doesn’t count.
Diogee, of Milo Murphy’s Law fame.
I don’t think that anthropororphic means what you think it means. Tom and Jerry are very much anthropomorphic. To be non-anthropomorphic, they can’t stand and move in human ways, walking on two legs, using tools, etc. It can talk, but it must still move like an animal. So a cartoon example would be the rabbits in Watership Down, or the dogs in 101 Dalmations.
But to make an attempt at an answer, a not very firm placeholder might be the cat from Bolt, or possibly the one from Kiki’s Delivery Service, or maybe the chameleon from Tangled, or…
Tom’s knees are always out when he walks. I’ve never seen a human walk like that.
What is your definition of ‘non-anthropomorphic’, because those two are totally anthropomorphic by any definition I know.
My favourite only mildly anthro animal is Lion from Steven Universe (he’s clearly of at least near human level intelligence, but he acts like an animal, has a sub-Lassie ability to communicate with the humans and Gems, and is definitely animal shaped, without much in the way of human-like expressions).
I would say it has to walk just like a human to be considered anthropomorphic. Tom and Jerry, Stitch, and Perry the Platypus all walk like animals. But if it talks in complete sentences, that would also be anthropomorphic. For example, Donkey is anthropomorphic even though he moves like a real donkey. Scooby is not anthropomorphic because he has the vocabulary of a one-year-old.
“1. described or thought of as having a human form or human attributes.”
“2. ascribing human characteristics to nonhuman things”
Not only “walk just like a human” XD
This includes walking, talking, or doing human like things like smoking, setting traps, reading newspapers, etc.
I didn’t know cartoons had a different definition of anthropomorphic than everyone else.
At first blush, I’d consider any animal not formed the same way as the natural animal to be anthropomorphic. (i.e. anything reshaped to look even slightly more human)
It’s also anthropomorphic to give them thought bubbles or speech bubbles or the ability to read or make plans… but hey it’s a cartoon 
The minute I saw the title, I said “But there’s no clear line. This is going to be a mess.”
But my vote is Snoopy.
(OG Snoopy – original as in pre-January 9, 1956, the day he first stood on two legs)
Did you read the full post? I consider Donkey anthropomorphic.
Not really, no. They walk like cartoon characters. They never walk on all fours (well, Perry might, I don’t watch Phineas and Ferb), they’re perfectly stable on their hind legs, and they don’t waddle, hop, or dance around unsteadily.
Calling a speaking feral more anthropomorphic than an anthro with a funny gait (not all that different from mine, frankly - my ankles are turned and my knees are shit, so I walk funny), even one who’s mute, is distinctly idiosyncratic.
Frisky the puppy, who was always innocently terrorizing Claude Cat in the old Warner Brothers cartoons. All he wanted to do was play, like nearly all puppies do.
Dino from the Flintstones. Except for that one cartoon, which I’ve tried to block from my memory, he doesn’t talk or act human-like. He’s just a prehistoric man’s best friend.
Did you read my full post? Put it this way. Non of the animals listed in this thread are fully non-anthropomorphic. They all have human like qualities or ascribed motives.
Oh, and Tom’s feet are plantigrade, whereas real cats are digitigrade. (Platypodes and mice are both plantigrade.)
Since the OP didn’t use anthropomorphic correctly anyway, it doesn’t matter who you pick. But I would steer away from the likes of Donald Duck, Foghorn Leghorn, Top Cat, or Disney’s Robin Hood, which are far more humanoid than, say, Bolt, Bambi, or Lady and the Tramp.
As for non-speaking, I think that narrows the options down too much.
Top Cat is my absolute favorite H-B cartoon, mainly because it’s an animated version of Sgt Bilko. Doesn’t get more anthropomorphic than that!