Oh boy, where to begin with this one.
Okay, I'm not sure if PETA is aware that Team Plasma is actually THEM in the Pokemon sense. Team Plasma talks a big game about releasing Pokemon and cease capturing or even interacting with them, all the while its members have Pokemon in Pokeballs and engage in battles. It is later revealed by their true leader that it was all a ruse in order to gain power by overwhelming the world with their caught Pokemon (and their hacked Hydreigon. Yes, check when it evolves, that's a hacked Pokemon!).
Similarly, PETA are only interested in the rights of WILD animals, in that they should be released from zoos and research facilities and protected in the wild. As far as domesticated animals/pets or mixed breed animals are concerned, they want them all to be taken away from human ownership and exterminated.
In terms of their little Black and Blue version, it completely misrepresents the game by being too violent and fighting against humans. Their game mechanics suck, too (seriously, how does a Pikachu using Quick Attack do more damage than Thundershock?).
So yeah, like the Tanooki suit incident, PETA is just garnering attention with the release of a new, popular game by creating an inaccurate mess of a game and stumbling over their own lack of understanding or simple research.