Sister Pat Farrell, the president of the Leadership Conference, said in an interview that the Vatican seems to regard questioning as defiance, while the sisters see it as a form of faithfulness.

“We have a differing perspective on obedience,” Sister Farrell said. “Our understanding is that we need to continue to respond to the signs of the times, and the new questions and issues that arise in the complexities of modern life are not something we see as a threat.”

These same conflicts are gripping the Catholic Church at large. Nearly 50 years after the start of Vatican II, which was intended to open the church to the modern world and respond to the “signs of the times,” the church is gravely polarized between a progressive wing still eager for change and reform and a traditionalist flank focused on returning to what it sees as doctrinal fundamentals.

The sisters have been caught in the riptide. Most of them have spent their lives serving the sick, the poor, children and immigrants — and not engaged in battles over theology. But when some sisters after Vatican II began to question church prohibitions on women serving as priests, artificial birth control or the acceptance of same-sex relationships, their religious orders did not shut down such discussion or treat it as apostasy. In fact, they have continued to insist on their right to debate and challenge church teaching, which has resulted in the Vatican’s reproof.

The former head of the church’s doctrinal office, Cardinal William J. Levada, said after his last meeting with the nuns’ leaders in June, just before he retired, that they should regard his office’s harsh assessment as “an invitation to obedience.”