This week, one arch-conservative Catholic website published a commentary saying that gay clerics needed to leave the priesthood “permanently.” Two traditionalist cardinals wrote an open letter decrying the “homosexual agenda” that they said was spreading throughout the church. And a gossipy 550-page book was set for release purporting to lift the veil on the double lives inside the Vatican, “one of the biggest gay communities in the world.”

The prevalence of mostly closeted gay priests has recently been portrayed in all manners, from the work of the devil to something the church should learn to embrace.

But church figures in Rome and beyond say one thing is clear: As Pope Francis opens a landmark conference at the Vatican on sexual abuse Thursday, the debate over gay priests is becoming a divisive undercurrent of the summit itself.

“Gay priests are in the cross hairs,” said Father James Martin, an American Jesuit who has advocated for the church to welcome LGBT members with more compassion.

The topic hints at the challenges for the Roman Catholic Church as it begins the most direct attempt in its history to address the problem of sexual abuse. Though abuse and sexuality have been found to have no correlation, according to widely accepted research, they have become intertwined on the ideological battlefield of the church — and Catholics of all stripes have descended on Rome this week, with some arguing that Pope Francis is overlooking homosexuality in diagnosing the root reasons for abuse.

“The church seems to have agreed, with a complicit silence, on a trivialization of homosexuality,” Jean-Pierre Maugendre, president of a French Catholic group, said at a news conference this week.

Among the nine speeches scheduled throughout the four-day summit, none appears dedicated to the topic of homosexuality. Francis — and his allies organizing the bishops’ meeting — tend to say abuse stems from “clericalism,” or the corrupted power of those who think they are on a pedestal. But some traditionalist prelates in the Vatican say the pope is risking a summit without credibility. They say the central problem is gay priests who break their celibacy and act on their attractions with other adults or with male teenagers.

“We turn to you with deep distress!” began an open letter to summit participants released this week by American Cardinal Raymond Burke and German Cardinal Walter Brandmüller — two of Francis’s highest-profile critics.

“Sexual abuse is blamed on clericalism,” they wrote, referencing Francis without naming him. “But the first and primary fault of the clergy does not rest in the abuse of power but in having gone away from the truth of the Gospel.”

For church figures who view abuse through the prism of homosexuality, a former Vatican ambassador, Carlo Maria Viganò, has become the flag-bearer. Viganò last year wrote a scathing letter describing “homosexual networks” in the church and the widespread coverup of the behavior of a former cardinal, Theodore McCarrick. On Saturday, McCar­rick was defrocked over alleged abuse of minors and adult seminarians.

Traditionalists sometimes point to a multiyear John Jay College of Criminal Justice study, which found that in more than three-quarters of American cases in which clerics abused minors, “same-sex acts” were involved, mostly with victims 11 and older. But the researchers also said that data did not show gay men to be more or less likely to abuse minors than heterosexual men. More recently, a German study analyzing seven decades of church abuse cases in the country found that the majority of victims were 13 or younger when first abused.

“Anyone who tries to make the argument that homosexuality is a root cause does so against all the research that has been out there,” Cardinal Blase Cupich of Chicago, one of the summit organizers and a close Francis ally, said in an interview.

Separately, in a Vatican news conference this week, Cupich pointed to the United States, where data shows a drop in abuse cases — not because of a crackdown on homosexuality, but because of better training in seminaries, stronger church guidelines and cooperation with criminal authorities.

In perhaps the most famous remark of his six-year papacy, Francis said about gay people, “Who am I to judge?” His remark was a stylistic departure from earlier pontiffs, under whom “homosexual tendencies” were labeled an “intrinsic moral evil.”

But Francis has not altered official church teaching on homosexuality and has reaffirmed the official ban on gay priests. There have been several recent portrayals, sensitive and otherwise, about the priestly life in those shadows. A detailed January New York Magazine article by Andrew Sullivan estimated that 30 to 40 percent of U.S. parish priests were gay, implying a profound contradiction given the institution’s teachings. Sullivan described the lives of these closeted men and theorized that widespread homosexuality in the priesthood had fed, unintentionally, a “poisonous” omertà, or code of silence: Gay priests who slipped up and had consensual relationships were vulnerable and therefore liable not to speak up if they learned about abuse.

“Mundane failings — like a brief affair — can become easily blurred with profound evils like child abuse,” according to the article. “If you expose a child molester to his superior, for example, he might expose your own homosexuality and destroy your career.”

In a much different exploration of the church’s gay culture, a book set to publish Thursday, “In the Closet of the Vatican,” explores the supposed hypocrisy inside the city-state’s ancient walls, portraying an institution that is outwardly chaste and sometimes anti-gay, but inwardly anything but. The book’s author, French journalist Frédéric Martel, says he interviewed almost 1,500 people — and 41 cardinals — for the book. But early critics have pointed out that it relies heavily on innuendo and stereotypes.

Martel writes that the more outwardly anti-gay a Vatican figure is, the likelier he “conceals” something. He devotes a lengthy passage to Burke, saying his bathroom is worthy of a “deluxe spa resort” and his outfits akin to those of a “Viking bride.” He quotes somebody saying Burke’s style is “typical of drag-queen codes.”

Burke did not respond to a request for comment.

Martin, the Jesuit priest, who read an advance copy of the book, said the portrayals won’t help bring about acceptance of gay priests.

“Entirely absent in the book is the faithful gay priest,” Martin said. “One thing the Vatican could do is admit the possibility of good, healthy celibate gay priests. Just a word from Vatican officials admitting that would be a good step forward.”

Stefano Pitrelli contributed to this report.