In the Reagan era, conservative Republicans felt they had a powerful ally in Pope John Paul II, whose forceful anti-communism and anti-abortion stances played out in American politics.

Today’s conservatives are apprehensive about Pope Francis, who has changed the tone and culture, not the doctrines, of the Catholic Church in less than two years as pontiff. He stresses, with passion and authenticity, a commitment to addressing poverty and income inequality more than the social issues that have dominated much of the Catholic debate in America.

John Carr, a former top official of the U.S. Conference of Catholic Bishops, notes that Francis’s message on abortion is “no obsession, no retreat.”

The pope helped broker the recent thaw in U.S.-Cuban relations, to the consternation of conservatives such as Florida Sen. Marco Rubio. Francis is determined to make addressing climate change a moral imperative for the world’s 1.2 billion Catholics.

This doesn’t mean that Francis is the poster pope for liberal Democrats.

“He’s challenging everybody,” said Carr, director of the Initiative on Catholic Social Thought and Public Life at Georgetown University. “Most Democrats haven’t been talking about poverty.”

He suggested that Francis’ effect is starting to change the conversation among Democrats, along with some conservative Republicans, such as House Ways and Means Committee Chairman Paul Ryan of Wisconsin.

Still, Francis’ message is unsettling to more than a few conservatives, particularly his focus on climate change and his initiatives to influence the United Nations’ conference in Paris this year. Some prominent Republicans, such as Senate Environment Committee Chairman James Inhofe, are climate-change deniers.

Some Catholic business leaders have complained about Francis’s emphasis on income inequality and the defects of capitalism. Ken Langone, the billionaire founder of the Home Depot and a major Republican donor, warned Cardinal Timothy Dolan of New York that if the pope kept up the drumbeat, some wealthy Catholics might stop giving to church causes. (“Liberals say popes don’t know anything about sex, conservatives say they don’t know anything about economics,” Carr observed.)

And Francis has rattled the U.S. church hierarchy, notably the bishops. American church leaders have long been advocates for the poor and immigrants. But these are edicts many conservatives felt could be ignored; the focus and priorities were the social issues, led by hardline prelates such as Cardinal Raymond Burke, the former archbishop of St. Louis, who refused communion to any Catholic politicians who weren’t on the right side of the abortion issue.

Francis removed Burke as head of the Vatican’s high court. Burke, a Francis critic, recently asserted that a “feminized” church, which permits altar girls, is responsible for a shortage of priests and some of the pedophilia crimes. Equally important, the pope chose Blase Cupich, the progressive bishop of Spokane, Washington, to be the archbishop of Chicago, the third-largest American diocese. He succeeds Cardinal Francis George, a conservative cultural warrior.

Garry Wills, a renowned historian and Catholic scholar, said the pope has sent a strong message to entrenched interests such as those that oppose Obamacare for offering contraception coverage, even though the vast majority of American Catholics practice birth control.

“Francis has condemned careerism, which will make the bishops pay more attention to Catholic lives,” Wills said.

The pope will visit the U.S. in September. He’ll go to Philadelphia and New York and probably Washington. If so, look for a visit to the White House, as well as to a soup kitchen or some other venue that serves the poor, and he might accept House Speaker John Boehner’s invitation to be the first pontiff to address a joint session of Congress.

Privately, some right-wing Republicans have grumbled about this invitation, but they can’t block it. It’s not hard to envision an exceptional moment in the Capitol as pro-choice Democrats squirm when the pontiff celebrates the sanctity of life and Republicans wriggle when the Holy Father talks about social justice, income inequality and the moral imperative of addressing climate change.

Albert R. Hunt is a Bloomberg View columnist.