Cannot kill invulnerable parrot with cookie in Creative mode

The bug

You cannot kill an Invulnerable parrot with a cookie in Creative mode. Expected would be that this is possible because you can damage invulnerable entities in other ways while being in Creative mode.

How to reproduce

1. Summon an invulnerable parrot

   /summon parrot ~ ~ ~ {Invulnerable:1b}

2. Switch to Creative mode an feed it a cookie

   /gamemode creative