But gestures like Cardinal Tobin’s are evidence that Pope Francis’ words are having an impact. Bishops now have latitude to focus on the more inclusive parts of the church’s catechism on homosexuals, such as the call to accept them with “respect, compassion and sensitivity.” They can follow the principle of accompaniment, meaning they can meet people where they are spiritually and build relationships that help them deepen their faith.

“It’s the beginning of a dialogue,” said Francis DeBernardo, the executive director of New Ways Ministry, a group that ministers to and is an advocate for gay Catholics. “The church leadership, for the past 40 years, has just been so silent, and unwilling to dialogue, and unwilling to pray with L.G.B.T. Catholics that, even though this isn’t the ultimate step, it’s a first step,” he said of Cardinal Tobin’s welcome.

Some church conservatives were wary, however. The problem, they said, was not the idea of welcoming — after all, Jesus welcomed all — but that the public embrace of such a group could be interpreted as the church’s acceptance of a homosexual lifestyle, which church teaching bans.

“Everyone is welcome in the church, but no one is accepted as they are,” said the Rev. Robert Gahl, a professor of ethics at Opus Dei’s Pontifical University of the Holy Cross in Rome. “While I am delighted that they went to Mass in the cathedral, I hope that Cardinal Tobin challenged them, as all good shepherds should, to live according to the teachings of Jesus.”

But Cardinal Tobin said in an interview last week that to combine his welcome with a criticism would not have been a full welcome at all.

“That sounds a little backhanded to me,” he said. “It was appropriate to welcome people to come and pray and call them who they were. And later on, we can talk.”

Showing just how sensitive the simple act of welcome could be, he said that after the Mass he had received a fair amount of visceral hate mail from fellow Catholics. Someone was even organizing a letter-writing campaign to call on other bishops to correct him.