Well most stories that change just one detail of the world, while the rest remains the same, don't hold up too well when taking a closer look. If animal-like people existed since the beginning, would we have pet shops? Maybe if they do have a pet like mentality but otherwise I would say humans and animal-people would have a different relationship.
But for a short story like this I think this is fine. Otherwise there are so many problems/factors one has to decide on. Easiest solution would be to say animal-people = humans + animal tails/ears but in this case it would be more like Centaur's Worries, so no pet shops.
Another simple solution are slave-races, pet like characteristics but much darker overall.
But if you want to keep more animal traits like lifespan, assumed intelligence, morals/ethics and stuff like this it becomes much more complex.
And now I have been thinking about it too much and even came up with an example xD.
For example: Cat People. The internet tells me cats out in the wild reach an age of 2-3, maybe 5, while house cats can reach somewhere between 10-20. A few exceptions can get older, but most die before 20. If we assume that humanized cats can take better care of themselves, lets say they all reach 15-20. A cat is considered a full adult with 2 years. Now if they have intelligence comparable to humans that puts them at an disadvantage, because they have less time to learn things. But how would a society work that as to consider a 2year old cat and an 21year (or 18) old humans as equal? Wouldn't humans screw the cats over?
But maybe the cats are quick learners and can learn thinks 5x as fast as humans. If we move the adult limit a bit, we could say that cats are adults with 4-6 years. Still weird from a human perspective.
And relationships. Would humans accept an adult human (21+) dating an adult cat (4+)? And wouldn't cats find it weird, that they can't date a human (under 21 or under 18)? Like a human and cat born at the same time might never be allowed to have an relationship with each other because the cat might be dead by the time the human is legal. Ignoring stuff like accidents and the like. I guess this is just like elves feel about humans in fantasy stories xD.
And one would have to decide stuff like this for all animal races, if they even exist. I mean, would there be dogs or only wolf-humans around? Would they live peacefully or fight with us? What about animals that can get much older than humans? Or animals that can reproduce like crazy. In fantasy stories humans often have the numerical advantage over older races, but now?
It's interesting to think about how society would have developed if all these human like races existed since the beginning. Would all of them be still around now? Would humans still exist? Would some races be treated as slaves? Would they even mind? What about mixed races? Are all animals humanized or only a few?
Anyway, way to much work^^