The society runs a museum at the parsonage in Haworth, the village in northern England where Brontë grew up with her sisters Anne and Charlotte, both of whom also wrote major novels, and her brother, Branwell.
The clash may seem, to paraphrase another literary giant, much ado about not much. But in an era when women the world over have broken through the walls of silence surrounding forms of patriarchal abuse, the row became a trending topic on social media. The issue was skating on the edges of an infuriating male habit to control what women say and do, some commenters said.
Mr. Holland’s post set off sharp reactions online, overwhelmingly in Ms. Cole’s favor. While he received some support for his post, many critics dismissed his comments as sexist and snobbish, noting that Ms. Cole had helped save a London bookshop and graduated from Cambridge. Others rejected his arguments with pithy obscenities.
Moreover, said Helen Small, a professor of English literature at Oxford, making assumptions about how Emily Brontë would have reacted was a stretch: Brontë is regarded as one of the most enigmatic figures in literary history because of the absence of a confessional narrative in her work.
“You can’t place her within the same contexts that other people operate,” Ms. Small said by phone on Friday. “There is so little evidence for what she thought — using her in this way is irrelevant.”
The issues raised by critics of Mr. Holland’s post would have been familiar to the Brontë sisters. They initially published their work under pseudonyms — some androgynous or gender-neutral — to protect their art from prejudice. (“Wuthering Heights” was first published under the pen name Ellis Bell.)
When Charlotte, the author of “Jane Eyre,” asked the poet Robert Southey about her work, he told her: “The daydreams in which you habitually indulge are likely to induce a distempered state of mind.” He added, “Literature cannot be the business of a woman’s life, and it ought not to be.”
For the anniversary of Brontë’s birth, on July 30, 1818, the museum asked Ms. Cole to make a film about Heathcliff, the antihero of “Wuthering Heights.” Her mandate was to “consider gender politics and women’s rights” in 2018, which also marks 100 years since British women got the right to vote.
Responding to the contretemps, Ms. Cole drew parallels with the sexism the Brontë sisters faced. “I find myself wondering, fleetingly, if I should present the short film I am working on for the Brontë Parsonage Museum under a pseudonym myself, so that it will be judged on its own merits,” she wrote.
Ms. Cole shot to prominence in the early 2000s as one of a crop of “otherworldly” models. She was the youngest woman to appear on the cover of British Vogue, at 16. She walked some of the most prominent runway shows before studying art history at Cambridge and dipping in and out of acting and activism.
In this, she followed in the footsteps of supermodel peers who in the late 1990s parlayed their fame into personal brands, including Cindy Crawford and Iman, who started businesses, and Christy Turlington, a graduate of New York University and Columbia who advocates for women’s health. Karlie Kloss, an active model, attends N.Y.U. and runs camps for girls, Kode With Klossy.
“I would not be so presumptuous as to guess Emily’s reaction to my appointment as a creative partner at the museum, were she alive today,” Ms. Cole said in her statement. “Yet I respect her intellect and integrity enough to believe that she would not judge any piece of work on name alone.”
But to Mr. Holland, Ms. Cole is hardly qualified to run in Brontë’s circles: He said the society should have appointed a distinguished female writer instead. (The society did include in the festival the poet and performer Patience Agbabi, the artist Kate Whiteford and the folk duo the Unthanks.)
In his post, Mr. Holland also took a dim view of Ms. Cole’s acting, recounting her performance as Helen of Troy at Manchester’s Royal Exchange Theater. “The play was so bad that it is the only one I have ever walked out of at the interval,” he wrote.
He also saw shades of nepotism, because the incumbent creative partner at the Brontë Parsonage Museum, Simon Armitage, wrote that play. Attempts to reach the Brontë Society were unsuccessful on Friday. Mr. Armitage did not respond to a message left with his agent.
In an email on Friday, Mr. Holland said he had been “taken aback” by the reaction to his post, and that he had been the subject of “bullying” online.
“I hate bigotry of all kinds and have fought against it all my life,” he wrote, “and now some accuse me of turning against Lily Cole simply because of her gender — a bizarre allegation as my heroes the Brontë sisters were women.”
“In light of the unwanted attention and abuse I’ve had online, I won’t be giving any more interviews,” he said, adding, “You understand.”