This type of thing is exactly why nobody takes PETA seriously. They probably have legitimate issues with the zoo, but this doesn't have anything to do with the Blue Jays. I can't think of an organization that's better than PETA at shooting itself in the foot.
Wow, he's been awful. 90 wRC+ and both Steamer and ZiPS think he's below-average true talent. With his defense now likely below-average in RF, he might be done as a viable everyday player.
The Royals have been acquiring a lot of flyball pitchers and great defensive outfielders, and it's worked pretty well in that spacious park. I imagine they value Dyson appropriately.