Elizabeth Gillies (Jade West) is the character that is accusing people of being a vegan. In reality Elizabeth Gillies is herself a vegan.
Among the many references to The Breakfast Club (1985) is the "Neo Maxi Zoom Dweebie" shirt that Robbie wears, which is a line from the film.
This episode is a direct parody of "The Breakfast Club"(1985)
One of the posters in the detention room has a poster for the movie 16 Candles. Another 80s film by the same creator of the Breakfast Club.