What church leaders may have told the scouts in private has not been revealed, but for the Boy Scouts, the threat was implicit that a liberal shift on homosexuality could drive away the Mormons, Catholics and other church partners, decimating the organization.

In 2000, when a challenge to the exclusionary policy was argued, unsuccessfully, before the Supreme Court, lawyers for the Mormons said that if the Boy Scouts were forced to accept openly gay members, the church would leave. In an interview this month, Mr. Beck said he could not speculate about a hypothetical situation, but he added, “We want to continue relations with the B.S.A. far into the future.”

The Mormon Church has sometimes faced lawsuits, along with the Boy Scouts, for past failures to stop sex offenders. Both the church and the scouts say they now have exemplary protection programs.

The civic and outdoor activities of scouting and the church’s more purely spiritual training are seamlessly combined: boys are divided into the same age groups in both settings, and their bishop-appointed scoutmaster on Wednesday night is also the man who guides them on Sunday through the stages of the Aaronic priesthood, in which boys 12 to 18 years old take on growing sacred duties.

The result is an enveloping world that promotes the Mormon version of achievement and traditional values.

“It’s tremendously cohesive, a system that works wonderfully — unless you don’t fit in exactly,” said Chase Barlet, 23, who grew up Mormon in the Denver area and quit scouting just before attaining Eagle in a silent protest against scouting’s ban on gay members. He is now an openly gay corporate lawyer in Canada and has left the Mormon Church.