DOWNSTAIRS IN THE dining room of the little South Dakota church, scores of men are standing around in small groups. Most are dressed in blue jeans and flannel shirts; a few wear old army fatigues. Many wear brimmed caps, some displaying the name of a tractor or farm implement dealer. The men are talking and drinking coffee out of paper cups. The conversation ranges from business concerns to their children's progress in school. Occasionally someone tells a funny story and a burst of laughter erupts from the group.

At first, an observer might assume they are here for a farmers' organization meeting, or perhaps a rural political caucus. But as the men take their seats and the meeting is called to order, it is clear that this is an altogether different sort of gathering. They have come together as they do twice a month—some from as...