I wanted the parrots to wear little top hats, so I made them wear little top hats.

This requires Optifine with the Custom Entity Models option enabled or it won't work.

Parrots on your shoulder will lose their hats, but will get them again when they get off. This is a problem with Optifine, there's nothing I can do to fix that, sorry. If anyone can figure out how to fix it, feel free to let me know!