And yet, this atmosphere of optimistic dialogue papers over significant divisions. Lutherans don’t agree with the Catholic Church on the authority of the pope or the way their churches should be governed by bishops. They themselves are not unified: The Lutheran World Federation, which represented Lutherans at the conference in Sweden, doesn’t actually speak for all Lutheran denominations. Prominent groups with more than 1 million members, such as the Lutheran Church-Missouri Synod in the United States, remain separate from even those who share a denominational name.

“It’s kind of a scandal, and it’s also a point of sorrow, because it divides the family,” said Eaton, whose more liberal denomination, the ELCA, is part of the Lutheran World Federation. “We also look silly to the rest of the world, I think, if we’re all fighting with each other.” Yet Samuel Nafzger, a former LCMS leader, wrote in a 2009 paper that doctrinal differences matter—and they’re best resolved directly, “not by ignoring them or by agreeing to disagree.”

Some within the Catholic Church are also skeptical of Pope Francis’s aggressive outreach to Christians of other traditions. “I think he’s tried to follow a cautious line in relationships with other Christian groups,” said Father Russell McDougall, the rector of Tantur Ecumenical Institute in Jerusalem, “because he realizes that if he gets too far ahead of his flock, he’ll lose them.” While the pope has worked on reaching out to Protestants, his ecumenical energy has more often been directed toward Eastern Orthodox churches, which deserve “special consideration” based on their close heritage with the Roman Catholic Church, according to Vatican II documents. There, too, some are skeptical. In Israel and elsewhere, for example, “some Eastern Orthodox clergy … believe ecumenism is the work of the devil,” said McDougall.

The goal of ecumenical dialogue can be hazy. Tantur was opened by Notre Dame in the 1970s in the wake of Vatican II to “assist the search for Christian unity and interchurch harmony.” And yet, McDougall said, some in the Catholic Church still think “ecumenism means, ‘Enter into dialogue with others to show them Catholicism.’” He believes that, more than ever before, “Christians now … recognize that our own narratives that we tell our congregations for catechistic purposes have been simplistic.” But living out that recognition can be rocky. “There still is a reluctance on the part of some Christians to pray with other Christians at all,” McDougall said. “The Eucharist is still a tender point … For the most part, Catholics don’t invite Protestants to communion in their churches, and the Orthodox don’t invite anyone.”

Even when leaders of different Christian traditions find theological agreement, “the churches don’t really know what to do with the results,” said Father Frans Bouwen, a member of a Catholic order called the Missionaries of Africa, or White Fathers, who run Saint Anne’s Basilica in Jerusalem. In his years overseeing a journal on ecumenism, Proche-Orient Chrétien, Bouwen has found that theologians and top Church leaders have more energy for ecumenical work than local religious leaders. “This is in some way disappointing,” he said. “The priests say, ‘We have done the work, but the churches do nothing.’”