This was in a homemade server, all vanilla. I tamed two parrots, a blue one and a grey one. I tried to put the blue one into my boat first. It didn't go inside, so I thought I'd drive over it with my boat to see if it would get in. It appeared to go underwater, but when I backed up, the parrot was nowhere in sight. The next time I did this, I successfully pushed the grey parrot inside my boat (although it seemed to be clipping instead of actually sitting in there) but when I drove backwards the same way it vanished too.

I'm kind of sad.