Seventeen-year-old New Yorker Hava Aaronson, a self-consciously observant Jew, is nonetheless unorthodox in many ways. She has spiked hair, loves punk culture, and punctuates her colorful, rebellious language with four-letter words (though she is reverently careful to refer to the Supreme Being as "G-d"). Her best friends are her confidant Ian, who is gay and not Jewish, and her platonic soul mate Moishe, who makes offbeat films and practices a kind of countercultural Orthodox Judaism.
In its original nature, the punk culture has been primarily concerned with individual freedom, which tends to create beliefs in concepts such as individualism, anti-authoritarianism, anarchism and free thought. Punk ideologies have often included a critical view of the world; seeing modern day societies as placing extensive limits on humanity.
"Never Mind the Goldbergs" is fiction, so I don't know if there are Orthodox punks - but if they do exist, I don't understand how they rationalize their existence. Of course, everyone is free to believe what they choose, but it seems to me that these people are confused about their beliefs since they appear self-contradictory.