In 1997, President Bill Clinton announced the beginning of a yearlong “Initiative on Race.” Arguing that the public needed to face “the implications of Americans of so many races living and working together as we approach a new century,” he established an advisory panel to facilitate a national dialogue on race.

The idea of encouraging communication between whites and minorities as a way to dismantle racism is not new. Since the 1980s, many businesses, universities, social organizations, and religious groups have undertaken cross-racial dialogues to help whites and minorities better understand why they often hold such contrasting views on race relations. During such discussions, whites and minorities are given a chance to see each other as individuals with a variety of backgrounds and opinions—an experience which can help to undercut stereotypes and prejudices, proponents contend. Well-...