I don't think anyone's making fun of anime. I used to like anime when I was a kid. My GAF name (which I've had for 10+ years) is based on an anime.
What I'm making fun of is the moe / kawaii designs of current anime with child-like characters or cat girls in bikinis. Or specifically the people that like them. It's the equivalent to Furry or MLP fans. It's creepy.
I've just heard it around a lot lately so was wondering. I don't think cat girls can help themselves to be honest. When they get to the closet they just reach for the bikini like a reflex.
Just look at anime today compared to the 80s and 90s. There's your answer.
Now that I think about it, I haven't watched any anime in quite a while.