If I look at my paperdoll with two parrots on my shoulder the right one glitches out and looks like it's sitting sideways. Likewise if you look at your inventory with the two parrots they appear to be sitting backwards. 

Steps to reproduce:

1.  ** Tame two parrots.
2.  Walk over them so they sit on your shoulders
3.  Open your inventory/look at your paperdoll

Right parrot appears sideways.