This isn't a fully-formed idea yet, but it seems to me that like, say, time-travel, you need to have your system down before you build your little furry cultures and the stories that happen in them. I mean, you can approach time travel in a couple of different ways: that the past already happened and any attempt to change it is doomed to failure, or that when you change the past you create a new time-stream and a new reality. There are different variations and nuances, of course, but these two schemes seems to comprise the main divisions of that trope.
So, for anthropomorphic animals, it seems to me that we are also faced with a choice between two main categories. In one, prey animals are the human-like protagonists and predators are more like monsters; in the other, predators are the human-like protagonists and prey animals are, well, still animals.
In a story about a brave and noble band of deer making their way through the forest to a new grazing area under the guidance of a stalwart leader and a sage elder, the wolves might be demonic pursuers providing a constant threat. In a story about a bold and heroic pack of wolves on a quest under the guidance of a courageous leader and a scarred elder, the deer would be... deer? I guess it's just hard for me to see how to make both the deer and the wolves people, since the one group routinely gets eaten by the other in a totally amoral, course-of-nature way. How could our wolf-warriors meet deer, negotiate with them, ask directions from them, and then eat them, without destroying the anthropomorphism?
It seems much the same in a household situation. If the mice are my characters, with little mice families and mice mayors and mice police and whatnot, the cat must be like a beast that lurks outside of town. But if my character is a philosopher-cat commenting on life from his windowsill lyceum, I don't know how to make mice the students that she just happens to occasionally devour.
Of course, this might be more about my limitations as a writer than the demands of logic. Aesop and Rudyard Kipling, of course, had talking animals that were still animals, but those stories were deliberately fabulous. If I recall correctly, in The Secret of NIMH, the owl is both a source of ancient wisdom and a predator; but Mrs. Brisby's interactions with him echo more to me the typical interactions between a hero and a dragon than a conversation between two people. And Brian Vaughn has lions and monkeys and deer all talking to each other even as some are eating the others in the great Pride of Baghdad, but that wasn't so much about anthropomorphizing animals as it was about animamorphizing the reader, I think.
So maybe what I am really talking about is a restriction I see on the construction of conventional genre stories using animal protagonists - when heroic fantasy or science fiction or picaresque adventure happens to feature people-like critters instead of people. The sort of rules-making that preoccupies me would certainly make it easier to write those stories, although it wouldn't necessarily make the stories any better. But I guess it wouldnt becessarily make them worse, either.
Remember, the Fantastic Mr. Fox ate chickens.