Command selectors cannot find shoulder entities.
→ You will notice that the parrot is not listed
Parrots don't die when doing /kill @e IF on shoulder
Parrot on shoulder not dying from commands
Sitting player shoulder parrots do not count as an entity
Parrots don't make any sounds when they are on your shoulder
Bees in bee hives/nests don't die from /kill @e command when in hive
Parrots do not dance when sitting on player shoulder