LAST July Lena Dunham, creator of the HBO hit series Girls, posted a heartfelt message on Instagram. “I have weathered a lot of micro-scandals but this one hurts MOST,” she wrote. Dunham had claimed that her former rescue dog, Lamby, had been abused by its former owners, but her claim was contradicted by the animal shelter she had obtained Lamby from.

More than four months later, Dunham is experiencing a much more serious “micro scandal”, this one of her own making. It has led many to question her liberal and feminist credentials, and even Piers Morgan has weighed in, asking: “Is there a more tiresome, tedious celebrity feminist alive today than Lena Dunham?”

The controversy began when actor Aurora Perrineau filed a police report accusing Girls writer and executive producer Murray Miller of raping her in 2012, when she was 17. Miller “categorically” denied the charge through his attorney.

Dunham and her fellow showrunner on Girls, Jenni Konner, issued a statement in which they said they had been “thrilled” to see “so many women’s voices heard and dark experiences in this industry justified” during the “windfall of deeply necessary accusations over the last few months in Hollywood”.

But they went on to defend Miller: “During every time of change there are also incidences of the culture, in its enthusiasm and zeal, taking down the wrong targets. We believe, having worked closely with him for more than half a decade, that this is the case with Murray Miller. While our first instinct is to listen to every woman’s story, our insider knowledge of Murray’s situation makes us confident that sadly this accusation is one of the 3% of assault cases that are misreported every year … We stand by Murray…”

The backlash was immediate. Writer Zinzi Clemmons accused Dunham of 'hipster racism', and said she would no longer contribute to Dunham’s feminist online site, Lenny Letter. “For all you writers who are outraged by what she did,” Clemmons wrote, “I encourage you to do the same. Especially women of colour.”

Clemmons went on to describe the “hipster racism” of many young women she had encountered while at college. “Many of these acquaintances were like Lena - wealthy, with parents who are influential in the art world … Back in college, I avoided those people like the plague because of their well-known racism … In Lena’s circle, there was a girl who was known to use the N word in conversation in order to be provocative.” In a tweet she added: “It is time for women of color--black women in particular--to divest from Lena Dunham.”

Dunham, who is 31, has an extremely privileged upbringing, having been born in New York City to parents who were both successful Manhattan artists. The Dunham family are cousins of the Tiffany family, prominent in the jewelry trade. She went to a private school, St Ann’s. A New Yorker profile in 2010, recorded her remarkable self-assurance: teacher Alex Darrow, who taught her English, said: “In about seventh grade, she came up to me and said, ‘I have heard good things about your class. I look forward to the Mr. Darrow experience.” She later graduated from Oberlin College, where she had majored in creative writing. While at college she made a number of personal video projects, which she posted online.

In 2010 Dunham wrote, directed and starred in Tiny Furniture, an independent, semi-autobiographical film, in which she played Aura, an arts graduate who returns to her mother’s home. The film, which also featured Dunham’s real-life mother, and her sister Grace, received glowing reviews and won several awards. Interestingly, Judd Apatow, who would become an executive producer on Girls, would tweet of Tiny Furniture: “I think [it] is good. But it does represent the Cinema of Unexamined Privilege, let’s face it.”)

Girls, which debuted on HBO in April 2012, really made her name. In HBO’s own words, this “fearless comedy tackles female friendship through the eyes of four 20-somethings as they attempt to navigate the unpredictable waters of adulthood in New York.” It was deservedly showered with awards and critical acclaim, even if some people were made uneasy by its all-white main cast.

In 2013 Dunham’s stock rose higher still when she signed a $3.7m contract with Random House for an intimate memoir, Not That Kind of Girl. But Dunham has also been known for a series of gaffes. Last year she said in her newsletter that the American footballer Odell Beckham Jr had ignored her at the Met Ball because she was insufficiently attractive to him; she apologised. She also apologised for saying in a podcast that she wished she'd had an abortion, as she wanted to better understand women who had had one.

Dunham has become a widely admired cultural icon but her privileged background undermines her position as liberal-lefty-feminist especially in the midst of current controversies engulfing showbusiness. She has apologised for her defence of Murray Miller, saying: “I now understand that it was absolutely the wrong time to come forward with such a statement and I am so sorry.” But critics have recalled that she had previously savaged Harvey Weinstein and, only on October 10, had written a New York Times piece on why survivors of sexual assault in the film industry should be supported and empowered. Some commentators have rallied to her defence: Giles Coren, the Times columnist, said the “ruthless purging” of her “seems weirdly Stalinist in its political opportunism”. But others - including many who admire Dunham’s career and her writing - are altogether less forgiving.