One whose snobbery is defined by opposition to perceived snobs, highbrow art, aesthetics in general or simply anything one does not like. Can be characterized either by reaction-formation favoring perceived lower-brow forms of art or quite separately by opposition to and persecution of anyone with any perceived aesthetic sensibilities whatsoever.
Anti-snob snob: Can you believe that guy likes Ingmar Bergman??? What a pretentious snob! You know he secretly hates it, nobody REALLY likes that stuff, he's just too much of a poseur to admit he just likes Brett Ratner like the rest of us.
Anti-snob snob: I don't like that uppity croissant and espresso bullshit, just give me a roll and strong coffee! (paraphrased from Mad Magazine's Simon & Simon parody)
Dad, stop pretending you don't like Thomas Pynchon and Fellini; Jesus, you've become such an anti-snob snob!