The clash reflects a fissure within conservative circles that deepened with the rise of the religious right in the 1980s, pitting those with a libertarian bent, who are most concerned with limiting government, against those, mainly led by evangelical Christians, who see same-sex marriage and abortion as acid tests.

A host of large and small church-based groups is boycotting the conference because of GOProud’s role. Its status was also cited by some secular groups, including the Heritage Foundation and the Media Research Center, when they dropped out this year.

Similar differences may bubble up as Republicans vie for the presidential nomination, although nearly all the hopefuls say they oppose same-sex marriage and abortion. Many of the likely candidates, including self-identified evangelicals like Tim Pawlenty, the former governor of Minnesota, and Rick Santorum, the former senator from Pennsylvania, have steered clear of the dispute and are speaking at the conference next month.

But Mr. DeMint, who attended last year, has refused an invitation this year. “With leading conservative organizations not participating this year, Senator DeMint will not be attending,” his spokesman, Wesley Denton, said in an e-mail. “He hopes to attend a unified CPAC next year.”

Former Gov. Sarah Palin of Alaska has not responded to an invitation to speak. Mike Huckabee, the former Arkansas governor, has in the past criticized CPAC for being too “libertarian.” He declined to comment for this article but will also not attend. The Tea Party movement has focused on fiscal rather than social concerns, and several of its leaders, including Representative Michele Bachmann of Minnesota and Senator Rand Paul of Kentucky, are scheduled to speak at the conference.

David A. Keene, the longtime chairman of the American Conservative Union and its annual conference, said that the conservative movement’s different strands had always argued but had come together when they needed to.