Scoutmaster Darrel Russell, of Weatherford, took his wife and five of their seven children to the rally. Russell said having gays in the scouting movement would be like mixing boys and girls.
"The whole idea is to protect our boys at all costs," Russell said, warning that if the ban is lifted "we're shutting down our troop."
President Barack Obama, an opponent of the policy, and Texas Gov. Rick Perry, an Eagle Scout who supports it, both have weighed in.
"My attitude is that gays and lesbians should have access and opportunity the same way everybody else does in every institution and walk of life," Obama said Sunday in an interview with CBS. As U.S. president, he is the honorary president of the BSA.
Perry, author of the book "On My Honor: Why the American Values of the Boy Scouts Are Worth Fighting For," said in a speech Saturday that "to have popular culture impact 100 years of their standards is inappropriate."
The board faces several choices, none of which is likely to quell the controversy. Standing pat would go against the public wishes of two high-profile board members — Ernst & Young CEO James Turley and AT&T Inc. CEO Randall Stephenson — who run companies with nondiscrimination policies and have said they would work from within to change the Scouts' policy.
Conservatives have warned of mass defections if Scouting allows gay membership to be determined by troops. Local and regional leaders, as well as the leadership of churches that sponsor troops, would be forced to consider their own policies. And policy opponents who delivered four boxes of signatures to BSA headquarters Monday said they wouldn't be satisfied by only a partial acceptance of gay scouts and leaders.