Joshua Harmon’s play “Bad Jews” has been packing the house at the Royal George Theatre in Chicago. The play premiered in October 2013 at the Roundabout in New York, and opened in London in January 2015. In Chicago, the play’s run has been extended seven times.

Lean, well-written and punchy, the play has an intriguing premise: Three cousins who are forced to share a studio apartment in New York the day after their grandfather’s funeral argue over who will inherit his Chai necklace, which he kept in his mouth during his two years in Auschwitz. The cousins’ disagreements reflect their deeper conflict over their approaches to Judaism. Liam arrives with his non-Jewish girlfriend, Melody, and is disdainful of Judaism, but he wants the Chai to propose to Melody with. Daphna is proud of being Jewish, wants to go to Israel to study to be a rabbi and marry her Israeli boyfriend, and feels that as the only Jewish-minded cousin, she is entitled to the Chai. Liam’s brother, Jonah, claims he doesn’t want to take sides and isn’t interested in the Chai. The play hits a nerve because it zeroes in on the anxiety of American Jewry today as writ large in the landmark Pew study about Jewish identity. Today’s high rate of intermarriage means American Jews are loved by non-Jews more than ever before — but not, perhaps, if they insist on their Jewishness. So what does this mean for the future of American Jews?

Harmon’s portrait of Daphna, the lone Jewish woman on stage, and by extension all Jewish women, relies on retrogade anti–Jewish woman tropes — nagging voice, excessive hairiness. That “Bad Jews” was written by a young Jewish playwright makes this feel like even more of a betrayal. Jewish leaders ruing the Pew study might want more Jews to be like Daphna, who decries intermarriage, values her Jewishness and doesn’t want it to be watered down in future generations. But Harmon has made her so unlikable — rigid, self-righteous, whiny. Even her womanliness is questioned: She is depicted as so undesirable that Jonah agrees that her Israel boyfriend must be a figment of her imagination.

In “Fighting To Become Americans,” the author Riv-Ellen Prell writes about how in the 20th century the gender stereotypes Jews create about Jewish men and women reflect our desires, longings and anxieties, namely our anxieties about our place in a pluralist nation. Jews of Prell’s generation, in the 1960s, could not become Americans and join the middle class “without forswearing their difference from other Americans in that class,” Prell writes. “For Jews, this longing to belong was inseparable from escaping a Jewish home that, decades before the Holocaust, had orphaned them through anti-Semitism.” Thus the stereotypes about Jewish women — the Jewish mother in the 1950s and ’60s (think “Portnoy’s Complaint”), the JAP in the ’60s, ’70s, ’80s and ’90s — become a repository for the traits Jewish men want to separate themselves from in order to successfully assimilate and join the middle class.

From her first words, Daphna’s voice is annoyingly nasal: reminiscent of Fran Drescher in “The Nanny.” In a rant when Daphna is offstage, Liam derides her as a “Super Jew” with “disgustingly hideous hair” and compares her to a dog “shedding again.” Mocking her for wanting to move to Jerusalem and shove “shofars in her hideous unused vagina,” he says her boyfriend probably only had sex with her once, woke up and thought it was a mistake. He hates her for holding up her Jewishness self-righteously, as if she is “on this spiritual enlightenment plane way above everyone else.”

Harmon’s depiction of Daphna reflects contemporary Jewish anxiety about our still-ongoing Americanization process. In Harmon’s portrait, her offensive righteousness represents the fears of today’s young Jewish men and women that if they are “too Jewish,” too insistent on Jewish particularity and the practice of Judaism, they will not be successful or loved.

In a final scene, blonde-haired, dim-witted Melody, who has appeared sweet, loving and accepting of her Jewish boyfriend throughout the play, insists on going to the hospital because the Chai, which Daphna has torn from Melody’s neck, might be rusty and thus a threat to her well-being. “It was in someone’s mouth!” Melody says. “I could have an infection.”

In the 20th century, Prell writes, the “relationship between Jews’ growing access to the wider culture and the increasingly strident images of Jewish women suggest that Jews may well feel that the price of admission to America is a rejection of critical aspects of oneself as a Jew. Projected onto mothers, wives, lovers, and partners are the loathsome and unacceptable qualities of affluence constantly represented as Jewish rather than middle-class.”

What’s disturbing about “Bad Jews” isn’t that Liam, a fictional character, projects cruelty and stridency onto Daphna but that Harmon himself does, that he doesn’t convey much warmth or heart or empathy for Daphna. Troublingly, perhaps the price of admission to commercial and critical success as a playwright in contemporary America is selling out Jewish women.

Laura Hodes is a writer and attorney based in Chicago.