Last fall, I traveled to Palo Alto, California, to meet the man with the unusual gift.

Some priests are known for their work among the poor, others for their learning, still others for decades of service to a parish. The Rev. C. John McCloskey III, a priest of the traditionalist Opus Dei order, has a different calling. He makes converts, often of the rich and Republican.

He has personally prepared for conversion to Catholicism, among others, Gov. Sam Brownback of Kansas; the Supreme Court nominee Robert H. Bork; the columnists Robert D. Novak and Lawrence Kudlow; the conservative publisher Alfred S. Regnery; the anti-abortion activist Bernard Nathanson; and Lewis E. Lehrman, an investment banker and former candidate for governor of New York.

McCloskey, 61, is hardly the only conservative priest or minister. But few have his knack for persuading political conservatives to adopt a different religion.

After military school, Columbia University, and a stint at Merrill Lynch, he joined Opus Dei and became a chaplain at Princeton University. He then ran the Catholic Information Center, an outreach ministry near the White House, where he introduced many Washington insiders to Catholicism. At his silent retreats in Virginia, Capitol Hill and K Street types see one another and nod.

When we think political influence, we think big money: the Koch brothers or Sheldon Adelson. McCloskey has taken a vow of poverty, but he has another kind of influence. He has helped shape the spirituality and the thinking of powerful people who have similar views about the market and social issues. Many of his converts know one another; it is a kind of club. As Pope Francis is breathing life into the Catholic left, McCloskey is defibrillating the Catholic right.

In Palo Alto, where Opus Dei sent him in 2013 after a period in Chicago, McCloskey and I shared a late-afternoon cocktail. He talked about his college years, his time on Wall Street, and his calling to become a priest. I had expected to be overwhelmed by charisma and instead was drawn in by gentleness. He listened more than he spoke, asked about my family, touched my arm several times.

Then, when it was over, McCloskey surprised me by asking that I not quote him. Opus Dei would not let him speak on the record.

So, to learn more about him, I turned to some of the men and women whom McCloskey has counseled.

Several discussed the pleasure he takes in conservatives’ company, and his quiet facility with networking. He gets referrals. To take one example, before Regnery ever met McCloskey, he knew about him from Kudlow and Novak, converts of McCloskey’s who, as conservative opinion columnists, knew pretty much everyone.

And in a Church whose priests are often on the left economically, McCloskey has a niche. He is a devout free-marketeer, a priest who defends the compatibility of pro-business policies and Catholic theology.

But more than anything, when I asked what made McCloskey so successful at persuading people to join the Church, I heard the answer, counterintuitive in its simplicity, that he befriends people, whether they ask for it or not.

“Once Father John gets his claws into you, he never lets go,” said Kudlow, who was fighting addictions to alcohol and cocaine when he met McCloskey in the 1990s.

“He reaches out and gives you that kind of companionship, and stays in touch,” Kudlow, now clean for almost 20 years, added.

Shortly after he began counseling Kudlow, McCloskey suggested that he go to church. Kudlow found that he loved Mass, and in 1997, he was baptized Catholic.

Brownback and Lehrman did not respond to requests for comment. Nor did the presidential candidate Rick Santorum, whose son was baptized by McCloskey. But Regnery, whose family firm has published William F. Buckley Jr., Ann Coulter, and Dinesh D’Souza, did respond, effusively.

In the 1990s, dissatisfied with the Episcopal Church, Regnery attended two weekend retreats run by McCloskey. They became friends, and in 2006 or 2007, he became a Catholic.

McCloskey knows that many men “don’t have any friends but their wife,” Regnery said. “He’s the kind of person, I guess, that if he weren’t a priest, you’d still want to befriend.”

In “Good News, Bad News,” his 2007 handbook on evangelism, written with Russell Shaw, McCloskey described the malady of “friendship deficit syndrome,” which he said was “a much bigger problem for American men than it is for American women.” And while he called it a problem, it is obvious that he sees it as an opportunity.

Men today, he wrote, move often for work, which is bad for friendship. All-male schools and social clubs have gone away, depriving men of separate spheres for bonding. Working women need their husbands at home, helping, instead of out socializing with men, which makes them worse husbands by depriving them of the opportunity to practice friendship.

Finally, he wrote, gay culture has hurt male friendship because, “especially in big cities, two men or a small group of men seen socializing” are likely “to draw stares from others and the unspoken question ‘I wonder if they’re gay.’” Thus, “many heterosexual men skip the hassles and the embarrassment by not socializing much with other men.”

As an anthropologist of urban male culture, McCloskey may hold eccentric views. As a political prognosticator, only time will tell: He has predicted that “culture of life” states, mainly in the South, might someday secede from the pro-gay, pro-abortion-rights rest of the country. As a campus chaplain at Princeton in the 1990s, he knew how to make enemies: He distributed lists of courses that Catholic students should avoid. Even many Catholic conservatives are wary of Opus Dei, which they see as secretive and bizarre — some of its lay members wear a spiked chain, called a cilice, around one leg — and some are repelled by McCloskey’s right-wing politics, about which he blogs regularly.

But as a friend, and as a teacher, he seems unimpeachable. A Princeton alumna, who asked not to be named because she works in Catholic circles where McCloskey is controversial, said he had introduced her to Catholic authors she had encountered nowhere else.

“Coming from a big public high school, GK Chesterton or Hilaire Belloc or Jacques Maritain or Evelyn Waugh — these are writers I wouldn’t have run across,” she said.

Meghan Cox Gurdon, the children’s book critic for The Wall Street Journal, had a religious awakening “in the autumn of 1998, on N Street in Georgetown,” she said. A Catholic friend suggested she talk to McCloskey.

“When I met him,” Gurdon recalled in an e-mail, “he was wearing a full-length black soutane. He was fearless, with the conviction of a person who has total command of his beliefs and facts.”

Did she have a theory on how he makes so many converts?

“Honestly, I don’t think any man converts another,” Gurdon wrote. “I really do think it is the work of Providence.”

McCloskey would seem to agree. He wrote in “Good News, Bad News” that “authentic conversion is the work of God’s grace.” Then again, the next sentence begins, “Grace works in countless different ways. …”