There are multiple issues that involve tamed (and only tamed) parrots and their behaviors. Tamed parrots will hover many blocks above the ground, far higher than they should, and are high enough where the player cannot interact with the parrot, nor can the parrot perch on the player. (A temporary fix is to walk far enough so the parrot teleports, in which it will teleport close enough to the ground and perch upon the player’s shoulder).
In addition, parrots do not “tire out” and return to the ground, which makes sitting them impossible.
Furthermore, when they are in a small enough space, they will not sit when prompted.
When a jukebox is playing, any parrots in the air start to dance in the air, rather than sitting down to start dancing. (This affects all parrots)
Edit: reloading a world does fix this issue. Please ignore.
In future, I would advise against grouping several issues like this into one report.