The Mickey Mouse Club was an actual thing. Fighting in the back of the comic, we see Britney Spears in what I think is a famous outfit from some music video. She was famously on the Mickey Mouse Club. Whoever she is beating up in the comic is probably another famous member that I am just unfamiliar with.
The joke here is basically "What if this happy fun time show was actually secretly like the novel/film Fight Club?"
Disney has made and destroyed many pop stars. Miley Cyrus explained in an interview that she had to act as crazy as possible for Disney to stop forcing her to tour as Hannah Montana.