COLORADO SPRINGS — One Wednesday afternoon last month, Jim Daly drove a couple of miles from his office at Focus on the Family to a classroom building on the University of Colorado’s local campus. Short as the trip was, it carried Mr. Daly beyond his theological and political comfort zone. Such disorientation was the whole point.

As the president and chief executive of Focus on the Family, Mr. Daly oversees a Christian ministry with an annual budget of $98 million, a paid staff of 655 and a fervently conservative view of the Bible and American social issues. Seated beside a philosophy professor at the university, Mr. Daly faced an audience of about 125 students and faculty members, some carrying protest signs: “Focus Isn’t My Family,” “No H8,” “Lez Be Honest Who Am I Hurting by Loving a Girl.”

For the next hour, through alternating moments of contrition and contention, Mr. Daly continued what has been the signal initiative of his term at the evangelical group: transforming an organization associated with the divisive strife of the culture wars into one that invites civil dialogue with its religious and ideological foes.

Mr. Daly did not come to the campus here to retreat from Focus’s opposition to same-sex marriage, which was largely the topic of the event, but to turn down the rhetorical temperature on the debate. “We’ve created an animosity,” he said in one emblematic moment of self-criticism. “We’ve said we hate the sin and love the sinner. But when you peel it back, sometimes we hated the sinner, too. And that’s not the Gospel.”