Custom super flat set to the extreme hills biome. The only passive mobs spawning are chickens.
I created a pseudo-skyblock map.
Layers, 5 water blocks, 1 blue glass.
Biome set to extreme hills
1 stronghold, (nothing else)
Build is up near Y70. Chickens spawn readily on grass but no other passive mob has spawned. I've killed all the chickens several times over the last few days.