Parrots do not imitate the sounds of peaceful animals. Livestock, Horses, Villagers, Bats, Squids, etc.

I expected the parrot to imitate any mob it is close to (other than other parrots.)

What happened instead was Parrots only imitate neutral and hostile mobs.

Steps to reproduce:
1. Spawn a few parrots in an enclosed area away from other mobs.
2. Spawn in any kind of peaceful mob in the same area.
3. Listen to the noises they make. They will continue to make their idle sounds.

They will group around and look at peaceful mobs as if they were trying to copy them like they do with others, but no noise is created.