Parrots on shoulders disappear when flying up in creative or spectator mode

The bug

When you start flying with a parrot on your shoulder, it will disappear when flying up.

Steps to reproduce

1. Spawn and tame a parrot
2. Go into creative mode
3. Allow the parrot to land on your shoulder
4. Start to fly
5. Fly up and notice the parrot disappears

Video showing how to reproduce.