First out of the gate to give him thumbs-up was Emeritus Pope Benedict XVI, whose historic resignation paved the way for Francis' election on March 13, 2013.
In a letter released on the eve of Francis' anniversary, Benedict publicly dismissed as "foolish prejudice" the opinions of critics who say Francis has no theological heft and represents a rupture from Benedict's papacy.
Benedict said a new Vatican-curated volume of books on Francis' theology "shows Pope Francis is a man of profound philosophical and theological training and helps to see the interior continuity between the two pontificates, with all the differences in style and temperament."
Francis frequently downplays the work of theologians, and his critics have flagged his cautious opening to allowing divorced and civilly remarried Catholics to receive Communion as a sign that dogma under the Church's first Jesuit pope is adrift.
Francis' supporters insist he is in complete harmony with church teaching and Benedict's doctrinaire papacy. They say Francis is merely emphasizing "discernment" to navigate complex pastoral situations.
But the debate is taking its toll. A poll published Tuesday in France's Le Figaro newspaper found a significant drop in the still-high support for Francis among church-going, practicing Catholics. The 86 percent who back him 12 percentage points lower than in 2015.
The poll, conducted by the BVA firm, paralleled the decline among practicing Catholics in the U.S. reported by the Pew Research Center.
The BVA survey said going forward, French Catholics wanted to see Francis better defend Europe's Christian roots amid an influx of refugees, to rethink priestly celibacy and to crack down on clerical sex abuse.
Cardinal Pietro Parolin, the Vatican secretary of state, acknowledged Francis had his critics. But he distinguished between "destructive, aggressive, really bad criticisms" that have to be accepted as a cross to bear and "constructive criticism" that can be helpful.
Francis has come under the most criticism for his handling of clerical sex abuse cases. He has intervened in canonical cases to reduce sentences for priestly offenders, has defended a Chilean bishop accused of ignoring abuse and has dismissed complaints about the bishop by Chilean victims as slander.
The pope also reneged on a plan to create a tribunal to judge negligent bishops, allowed his advisory commission on the issue to lapse and didn't reappoint several of its most outspoken leaders to new terms.
"He has had more difficulty in that issue than he has on being welcoming, being uplifting, being simple, being frugal," said the Rev. Michael Martin, a 77-year-old missionary priest in Manila. But he added that Francis "has brought extraordinary transformation" to the church at a challenging time.
Indeed, in the streets, the pope remains beloved.
"I think he's an extraordinary person," Juliana Galeano, a 46-year-old geographer said while picking up her son at a Catholic school in Sao Paolo, Brazil. Unlike many church leaders who "think it's the Middle Ages," Francis wants to move the church forward, she said.
Gerald Bareebe, a Ugandan academic who described himself as a progressive Catholic, said he wants Francis to push the envelope further on the thorny issue of priestly celibacy and married priests.
"In Uganda, not a year passes without media houses carrying stories of priests who are caught in marital affairs," Bareebe said. "And these cases have become common partly because priests are forced to take mandatory celibacy. The church should save its face and allow priests who want to marry and continue serving God to do so."
The issue is likely to feature in some of Francis' initiatives in the future. A church meeting is scheduled for 2019 on spreading the faith in the Amazon region of South America, where an acute priest shortage has led to calls for married priests.
AP writers Rodney Muhumuza in Kampala, Uganda, Jim Gomez in Manila and Sarah DiLorenzo in Sao Paolo contributed.
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