Invisible parrots turn visible when sitting on shoulder

Invisible parrots become visible when sitting on a player's shoulder.

Steps to Reproduce:

[Step 1] Spawn a parrot
[Step 2] Tame the parrot
[Step 3] Throw a splash potion of invisibility on the parrot
[Step 4] Put the parrot on your shoulder
Observed Results:

The parrot turns visible when picked up.

Expected Results:

The parrot remains invisible.

Screenshots/Videos:

Notes:

The bug doesn't affect gameplay that much. I made a new world to test the bug.