ONE emerged from a crisis conclave, the other was elected after the strangest campaign in recent American history. Both have upended traditions and reached outside the usual channels to speak to the concerns of ordinary people. Donald J. Trump and Jorge Mario Bergoglio, the president and the pope, are the world’s most famous populists. But they are in conflict.

To grasp why Pope Francis has become the flag-bearer of the global anti-Trump resistance, consider his Feb. 17 appearance at a university campus in Rome, where one of the students who asked him a question was a Syrian woman, Nour Essa. The pope knew her well. Hers was one of three families, all Muslim, he had brought back with him on the return flight from his visit to a refugee camp in Lesbos, Greece. He has helped dozens of refugees make new lives in Italy. Two families live in the Vatican itself, whose high walls and fortress features are these days at odds with the border-dissolving pope within.

In the courtyard of the university, Roma Tre, where Ms. Essa has won a scholarship to study biology, she asked Francis to respond to Europeans who believe migrants threaten the continent’s Christian culture. Migration, he told her, is not a danger but a challenge, a spur to growth that has expanded Europe’s culture, not weakened it.

“When there is this welcoming, accompaniment, integration, there’s no danger with immigration,” he said. “A culture is received and another offered. This is my response to fear.”