When Pope Francis arrives in the United States on Tuesday, he’ll greet a flock in transformation, its future tied to the growing influence of Hispanic immigrants and a generational decline in religious affiliation.

Francis will also encounter an American church that relates less with traditional Catholic stances on marriage and family, from divorce to out-of-wedlock births to same-sex marriage.

In other words, U.S. Catholics are evolving with the modern world more quickly than the church itself. And many are anxious to see how the popular pope will tailor his message to them.

“Catholicism in America today is a more diverse population,” said William Dinges, a professor of religious studies at Catholic University. That trend, he said, covers not only who American Catholics are, but what they believe, and how they view themselves in relation to the church.

Consider this portrait sketched out by the Pew Research Center, based on recent surveys:

  • A growing proportion of American Catholics — 34 percent, up from 29 percent in 2007 — are Hispanic, and more than a quarter were born outside of the United States.
  • Half of those who said they were raised Catholic have left the church. Of that group, 41 percent never returned, though many of them have become “cultural Catholics” who still identify with the religion in some way.
  • One in four have gone through a divorce, and four in 10 said they’d lived with a romantic partner at some point in their lives. Six in 10 said Catholics who are cohabitating or had been divorced and remarried without getting an annulment should be able to receive communion.
  • Two-thirds of Catholics said it was acceptable for same-sex couples to raise children. Forty-three percent said a gay or lesbian couple raising children was as good as any other kind of family. And 46 percent said the church should recognize same-sex marriages.
  • Asked whether homosexual behavior was a sin, 39 said no, and 44 percent said yes.

“Overall, Catholics look a lot like the general public on these questions,” said Jessica Martinez, a senior researcher at Pew. “The church has traditionally frowned on things like cohabitation and children being raised by gay parents. But, like many U.S. adults, more U.S. Catholics have experienced things like divorce and living with a non-married partner, or know someone who has.”

Pew also touched upon another thorny issue for the American church: the size of its membership. The pollsters estimated that there were about 51 million Catholic adults in the United States in 2014, or about 20.8 percent of the population — down about 3 million people from its 2007 survey.

That drop, Pew said, reflects a widening gap between the number of people who have left the church and the number of those who join or return — and a surge in the number of young Americans who claim no religious affiliation at all.

Other polls have not recorded a decrease. Gallup and the Public Religion Research Institute, for instance, have the proportion of Catholics among the U.S. population remaining relatively steady.

Mark Gray, a senior research associate at the Center for Applied Research in the Apostolate, said he was puzzled by that aspect of Pew’s findings.

“We see no decline in the Catholic population,” he said.

Gray said he has noticed declines in the Northeast and Midwest, but they have been offset by growth in the South and West. “It’s simple demographics — migration, immigration, places where America is growing in general,” he said.

Immigration has always been pivotal to the growth American Catholicism; before the influx of those from Latin America, its ranks swelled with Catholics from Europe.

The most recent wave of Hispanic immigrants is propping up the U.S. Catholic population, Dinges said. Without them, there’d be a pronounced decline, he said.

Six out of 10 American Catholics told Gallup this year that the country should give undocumented immigrants a way to become citizens. On that issue, they appear to be on common ground with Francis, who has urged compassion for the world’s immigrants, including those who enter the United States illegally.

American Catholics’ evolution on family and social issues — divorce, same-sex marriage — goes far beyond the church’s formal positions, but that gap may be narrowing. The Pope has expressed views that appear to indicate an openness to revised doctrine.

There is less apparent agreement on the environment, another of Francis’ signature issues.

Earlier this year, the Pope Francis issued a statement, or encyclical, blaming humans for global warming, linking the destruction to rampant materialism, and calling for radical reform.

Pew’s latest survey of American Catholics took place few weeks before that statement was made public. But the responses are telling: just 23 percent said it was a sin to use energy without considering the environment, and less than a third said working to address climate change was essential to what being Catholic meant to them.

Those differences aside, Francis remains widely popular among American Catholics: Pew found earlier this year that 86 percent had a favorable view of him.

That enthusiastic following echoes around the world, and has spawned a concept called “The Francis Effect” — the pope’s potential for drawing more people to the church, reframing decades-old culture-war battles, even influencing elections.

But that’s all speculation. For now, American Catholics are just happy he’s coming to visit.