But the buildup to the meeting between the two men in Rome on Wednesday has focused less on their shared sentiments and more on the many things that divide them. In myriad ways, Trump and Francis are almost diametric opposites.
The contrasts can be painted in both broad and tiny strokes. Trump is a flamboyant real-estate-mogul-turned-reality star-turned-politician who advanced his career through opportunistic gambles. His political views have rarely been consistent or tethered to a strong moral compass. The pope, meanwhile, worked his way up the ecclesiastical ranks in Buenos Aires and eventually reached the Vatican with a perennial commitment to the uplifting of the poor and marginalized.
That ethic has animated Francis's tenure at the head of the Catholic Church — and it has placed him at odds with Trump.
Consider the pontiff's compassion for migrants and refugees. Well before the West's far right scare-mongered about the "hordes" of migrants arriving at Europe's gates, Francis was raising awareness of the plight of asylum seekers drowning in the Mediterranean. He washed the feet of migrants trapped in temporary camps and personally transported Syrian refugees to safety in his own plane.
On a 2016 visit to Mexico, Francis indirectly attacked Trump's rhetoric on the campaign trail. "A person who only thinks about building walls, wherever they may be, and not about building bridges, is not a Christian," Francis said. Trump fired back, calling the pope's remarks "disgraceful."
Francis has also taken aim at the brand of right-wing ultra-nationalism that helped fuel Trump's political rise as well as that of other far-right parties in Europe. Speaking in Cairo last month, he said that the pursuit of peace was not helped by "demagogic forms of populism."
The pope is no defender of the European status quo. In 2014, he delivered a lengthy rebuke of capitalism and neoliberalism at the European Parliament, pointing to economic forces that deepened inequality and threatened to sap the continent of its vitality. He seemed to specifically object to the excesses of high finance.
"We encounter certain rather selfish lifestyles, marked by an opulence which is no longer sustainable and frequently indifferent to the world around us, and especially to the poorest of the poor," Francis said.
The pope wrote a whole encyclical, or papal letter, calling for global action on climate change — and chided climate skeptics for their "denial" and the international community for its relative inaction. Trump ranks among the skeptics; he seems determined to roll back years of environmental regulations on big business while also harboring plans to withdraw the United States from the Paris climate accords.
And while Trump fixates on American military strength and its capacity for unrivaled devastation, Francis embraces the cause of peace at every turn.
During a speech to Congress in 2015, Francis hailed Dorothy Day, an early-20th-century American pacifist, and commended her "social activism" and "passion for justice." Trump's right-wing equivalents at the time deemed Day a communist sympathizer, nicknaming her "Moscow Mary." FBI Director J. Edgar Hoover described her as a "very erratic and irresponsible person."
When the United States dropped a gigantic bomb on a suspected militant base in Afghanistan, boosters of the Trump administration celebrated the act as evidence of a new president who is willing to unleash the full potential of the American military on its enemies. But Francis was aghast at the breathless media reports that dubbed the weapon the "Mother of All Bombs."
"I was ashamed when I heard the name," he later told an audience of students at the Vatican. "A mother gives life and this one gives death, and we call this device a mother? What is happening?"
Not surprisingly, as my colleagues report, figures within the Trump camp are concerned about the depth of the divergence. The Wednesday meeting, though, is expected to be brief and probably sculpted around points of convergence, such as their mutual interest in the defense of religious minorities in the Middle East. Francis, for his part, has said he would not "make a judgment" of Trump before hearing out the American president.
"Should they pull off a congenial discussion, it could serve as a much-needed diplomatic salve for the American leader," The Washington Post's Anthony Faiola and Julie Zauzmer wrote. "A gaffe, meanwhile, could quickly stoke fresh controversy for a president facing a mounting crisis at home."
Clergy in Rome have their own concerns.
"The Vatican is just concentrating to see how and if there will even be a final communique," said Marco Politi, a Rome-based Vatican watcher, to my colleagues. "For me, this meeting is only the beginning of what is becoming a difficult and complex relationship between the Holy See and the American presidency."