A non-conformist is someone so obsessed with being different that they go to great lengths to avoid social norms; typically, you can identify them in a shopping mall because they all dress alike, listen to the same non-conformist music, and read the same non-conformist literature.
As it happens, it is also non-conformist to have any sense of self-awareness or irony beyond surface-level sarcasm and "snark".
"Who the hell are those guys?"
"They're the non-conformists."
"How can you tell?"
"Because they've all got blue hair and nose-rings."