I don't think they're making fun of animal cruelty, but what I think they are doing is making fun of animal activists. The reason they do this is because of a bunch of perceived (but untrue) relations with animal activism.
I think we can also go deeper into the problem and take what Nic said. It's the internet so jokes are made, as novaAurora said, but more so a certain amount of "meme" status is gotten from animal cruelty because of PETA. PETA have a lot of radical ideals, ideals that seem silly and they don't seem to care about their public image anymore, this causes them to do a lot of very intrusive demonstrations that can get them a lot of hate. As well, the severity of these demonstrations on, in the public, seemingly trivial issues (like a pet shops name for example) gives them a comical approach and to the normal anonymous internet user, it gives PETA a meme status as something to be made fun of.
Things like south park, that pokemon game, the media publicizing all the stupid things PETA tried to get people to change, it all adds to the internet social idea that PETA is bad. More so, a lot of people who aren't bothered to get educated in the problem (and that's a lot of people btw) assume PETA and animal cruelty activists are one of the same, this isn't true but this is what a lot of people generally believe on the internet. That if you're an animal activist, then you "hug trees", "hate pokemon" and so on, obviously this is all ridiculous but to an uneducated person they are true. As well, there's a whole vibe on facebook with people sharing those statuses that say "Like or share this post and facebook will donate $1 to stop animal cruelty", a lot of people these days are smart enough to realize those posts aren't truthful, and they relate the scamming post with animal cruelty indirectly. (This goes with a whole lot of other things, the internet and medias perceived smugness of environmentalists and even hipsters, saying hipsters are vegan and what not)
So the idea is that there is so much reason why uneducated people would make fun of animal activists on the internet, most of it is only from a few select groups that unfortunately cloud out the majority, but it happens and people see only the ridiculous sides of animal activism than the truer sides of it. So people make fun of it, to them animal activism becomes a joke, and it's really unfortunate that the more severe animal activists like PETA who do some ridiculous things cause so much problems for the things they are trying to achieve. They are actually causing animal activists to get a bad name which is damaging their end goal.