In August, the most senior leaders of the Mormon Church are expected to meet and discuss a decision with profound consequences: whether to end a 100-year relationship with the Boy Scouts of America that has helped shape both institutions.

This is not what the Boy Scouts hoped would happen on Monday when they officially lifted their ban on gay adult leaders but said conservative religious sponsors of local packs and troops could pick leaders who shared their beliefs, even if that meant limiting these voluntary positions to heterosexual men.

In adopting the new policy, the Scouts’ national board hoped to quell the growing turmoil over its position on gay leaders. But a day later, the Scouts were still torn by the issue, largely because the Church of Jesus Christ of Latter-day Saints, which alone sponsors units involving one in five scouting participants, said it might leave the Boy Scouts altogether.

The compromise policy appeared to work in the case of Roman Catholics, whose scouting units account for 10 percent of the 2.4 million total youth members at the end of last year. In a statement late Monday, a Roman Catholic committee that acts as a liaison with the Boy Scouts urged Catholic churches to continue sponsoring Scout troops, despite the decision to permit openly gay leaders.