VATICAN CITY — The Francis Revolution is under way. Not everyone is pleased.

Four months into his papacy, Francis has called on young Catholics in the trenches to take up spiritual arms to shake up a dusty, doctrinaire church that is losing faith and relevance. He has said women must have a greater role — not as priests, but a place in the church that recognizes that Mary is more important than any of the apostles. And he has turned the Vatican upside down, quite possibly knocking the wind out of a poisonously homophobic culture by merely uttering the word “gay” and saying: so what?

In between, he has charmed millions of faithful and the mainstream news media, drawing the second-largest crowd ever to a papal Mass. That should provide some insurance as he goes about doing what he was elected to do: reform not just the dysfunctional Vatican bureaucracy but the church itself, using his own persona and personal history as a model.

“He is restoring credibility to Catholicism,” said church historian Alberto Melloni.

Such enthusiasm isn’t shared across the board.

Francis’ predecessor, Benedict XVI, had coddled traditionalist Catholics attached to the old Latin Mass and opposed to the modernizing reforms of the Second Vatican Council. That group greeted Francis’ election with concern — and now is watching its worst fears come true. Francis has spoken out both publicly and privately against such “restoratist groups.”

His recent decision to forbid priests of a religious order from celebrating the old Latin Mass without explicit authorization seemed to be abrogating one of the big initiatives of Benedict’s papacy, a 2007 decree allowing broader use of the pre-Vatican II Latin liturgy for all who want it. The Vatican denied he was contradicting Benedict.

“Be smart. There will be time in the future for people to sort what Vatican II means and what it doesn’t mean,” Rev. John Zuhlsdorf warned his traditionalist readers in a recent blog post. “But mark my words: If you gripe about Vatican II right now, in this present environment, you could lose what you have attained.”