I was sure that was supposed to keep strays/wild horses/etc. from spawning. It doesn't make sense that they're there but can't be adopted... Well, I guess I learned something. The funny thing is that in all my time playing, I didn't previously notice that unchecking the box still allowed them to spawn. I feel very unobservant!
Edited to add: I have started up a new game in a completely clean, factory reset area. This time I am playing in Moonlight Falls. I have made my Sim an animal lover. I will be attempting to use the Pet interaction in this game, just in case it might have been the eye replacers or something that somehow caused the bug. May use some testing cheats for teleportation, lifetime rewards, etc. to speed things up.