Since 1.12 released (Which was the version when Parrots were added), Parrots wouldn't dance if a Music Disc is inserted before they spawned, yet the Allay does dance if a Music Disc is inserted before being spawned. Parrots will start dancing when being spawned after a Music Disc starts playing on Bedrock Edition, so I had this feeling deep down it was probably a bug. (I cannot upload the video because the file size limit is too small.