I don't like anthromorphic animal races either. Apart from being lazy design, imho they most often aren't consistent with the game world. I always feel like their existence would imply there being offspring with regular humans and the more you mix them, the sillier it gets. So at the start its half-dogpeople and then you get quarter-dogpeople and so on.
It doesn't even allow for characters that couldn't be human themselves in the first place. So you live with dogs because you have a dog head - a human could live with dogs as well.
Elves, Dwarfes and halflings aren't that original either, because they are humanlike as well, but at least you can imagine them having the same ancestors as humans, just having evolved differently (although this is a magical world where technically "everything goes", that is still way more plausible).
To be honest, I don't even need any humanoid races besides humans at all. Games like fire emblem show that a low fantasy can work as well, where its more about political conflict. Gothic comes to mind as well.
Now what would be interesting to play would be werepeople, but without animals. Lets say there is a whole country of cursed humans which are forced to transform into some kind of ...something different at certain points. So you had the chance to play as them, and at random points during fights, your heritage would take over you. That would give you bonuses and disadvantages and you can't control the transformation (but it wouldn't strip your control of the char).
No matter what they transform into (cliche demons, or have their personality inverted or something like that), the implications of this curse on the lifes of that people already sound more intriguing and interesting to me than anything that horse-head mentality could ever give.