Both Team Plasma and PETA are major organizations that are concerned with the well-being and living conditions of Pokémon and animals respectively. However, the most important issue that these two groups create is their ideology on how these creatures should be viewed; namely, that Pokémon and animals have the same right to live as human beings and, as such, should be treated as equals.
The problem that arises from this statement, of course, is that this is indicative of a severely anthropocentric philosophy. While their views on how animals should be treated are certainly a valuable and important concept to keep in mind when dealing with Pokémon and animals, this creates a space where the actual desires of the Pokémon are being pre-determined. As later seen in both Pokémon and, admittedly anthropocentric, views on human-animal relations, the ability of these non-human entities to co-exist with us can come into conflict when radical ideologies attempt to generate a solid rift and, in fact, separation between the lives of humans and these creatures.