“I think statements like the Vatican statement are designed to pretend that gay men are not in the priesthood, and to sort of uphold the myth that all priests are heterosexual, when the reality is far from that,” Mr. DeBernardo said.

The Rev. Warren Hall was fired from Seton Hall University’s ministry in 2015 after he came out as gay. In 2004, the Rev. Frederick Daley, now a pastor at All Saints Parish in Syracuse, came out, angered by what he called the “scapegoating” of gay priests during the church sexual abuse scandal.

Father James Martin, a Jesuit priest who has written a book called “Building a Bridge,” about L.G.B.T. Catholics, said that between 20 percent and 30 percent of Catholic priests are celibate gay men and that a larger reason they have not been public about their sexuality is homophobia in the church.

“As more and more Catholics come out, more and more families are affected, and they bring their hopes and desires into parishes,” he said in a telephone interview on Wednesday. “You see this new opening,” he said. “It is really extraordinary.”

Father Greiten, who was ordained in 1992, wrote that he had carried the “heavy burden” of keeping his sexuality a secret because of the church’s teachings, saying that each time he wanted to speak out he was challenged or discouraged by other priests and church leaders.

He said that before coming out he had informed Archbishop Jerome E. Listecki of Milwaukee of his plans. The priest also delivered the news to his parishioners during Sunday services, at which he was given a standing ovation, according to a report in The Milwaukee Journal Sentinel.

“We need healthy role models to be out there, to be able to say there is nothing wrong with being gay,” Father Greiten told WTMJ, a local news station, on Tuesday.