Prior to Monday's announcement, the BSA conferred with some leaders of these religious groups, including the Rev. Frank Page, who leads the Southern Baptist Executive Committee.
According to Roger S. Oldham, a spokesman for the executive committee, Page then wrote to the Scouts "expressing his tremendous dismay at the decision."
"They had been working for months on this proposal and just days before they informed us," Oldham said in a telephone interview.
If the Scouts proceed with the change, Oldham said, SBC leaders were likely to issue a statement "expressing disappointment and encouraging our churches to support alternative boys organizations."
Neither the Catholic Church nor the Mormons' Church of Jesus Christ of Latter-day Saints issued official statements as to how they would respond.
Said Sister Mary Ann Walsh, a spokeswoman for the U.S. Conference of Catholic Bishops, "The bishops hope the Boy Scouts will continue to work under the Judeo-Christians principles upon which they were founded and under which they have served youth well."
Were the change adopted, said Deron Smith, "there would no longer be any national policy regarding sexual orientation, and the chartered organizations that oversee and deliver Scouting would accept membership and select leaders consistent with each organization's mission, principles, or religious beliefs.
"BSA members and parents would be able to choose a local unit that best meets the needs of their families," he said. "Under this proposed policy, the BSA would not require any chartered organization to act in ways inconsistent with that organization's mission, principles, or religious beliefs."
The announcement came shortly after new data showed that membership in the Cub Scouts -- the BSA's biggest division -- dropped sharply last year, and was down nearly 30 percent during the past 14 years.
According to figures provided by the organization, Cub Scout ranks dwindled by 3.4 percent, from 1,583,166 in 2011 to 1,528,673 in 2012. That's down from 2.17 million in 1998.
The Boy Scouts attribute the decline largely to broad social changes, including the allure of video games and the proliferation of youth sports leagues and other options for after-school activities.
However, critics of the Scouts suggest that its recruitment efforts have been hampered by high-profile controversies -- notably the court-ordered release of files dealing with sex abuse allegations and persistent protests over the no-gays policy.
The BSA's overall "traditional youth membership" -- Cub Scouts, Boy Scouts and Venturers -- totaled 2,658,794 in 2012, compared to more than 4 million in peak years of the past. There were 910,668 Boy Scouts last year, a tiny increase from 2011, while the ranks of Venturers -- a program for youths 14 and older -- declined by 5.5 percent.
In addition to flak over the no-gays policy, the Scouts have been buffeted by multiple court cases related to past allegations of sexual abuse by Scout leaders, including those chronicled in long-confidential records that are widely known as the "perversion files."
Through various cases, the Scouts have been forced to reveal files dating from the 1960s to 1991. They detailed numerous cases where abuse claims were made and Boy Scout officials never alerted authorities and sometimes actively sought to protect the accused.
The Scouts are now under a California court order, affirmed this month by the state Supreme Court, to turn over sex-abuse files from 1991 through 2011 to the lawyers for a former Scout who claims a leader molested him in 2007, when he was 13. It's not clear how soon the files might become public.
The BSA has apologized for past lapses and cover-ups, and has stressed the steps taken to improve youth protection policy. Since 2010, for example, it has mandated that any suspected abuse be reported to police.Associated Press writers John Seewer in Toledo, Ohio, and Rachel Zoll in New York contributed to this report.