It might seem gatekeep-ey, but it's aimed at people who say stuff like "Oh, I cried when I saw that puppy dead in the road! It broke my heart, I'm just such an animal lover!" while they're draped in the skin and fur of three other animals that were killed for fashion.

I get the point if the comic, but the nuance is missing. "Animal lover" can also be meant in another sense: a person loves nature and studying the ecosystem, and appreciates its aesthetic beauty. They might consider themselves an animal-lover, while not empathizing with animals as individuals and having no qualms about killing them for entertainment. That person might rightly feel gatekept by this comic because of the way it's worded. You can love animals like you love math, academically, or you can love them like friends. The comic is trying to specifically call out people who claim to be in the second group.