Specifically, activists are asking why the International Olympic Committee -- with a credo of "sport for all" -- welcomes in its ranks scores of nations that ban gay sex. For the IOC, which has taken actions in the past to combat racism and sexism, it's a new civil rights challenge likely to linger long after the upcoming Summer Games in London.
"The IOC needs to come out of the closet," said prominent British human rights lawyer Mark Stephens. "Sport for all means all -- irrespective of color, gender or sexual orientation. It's a matter of human dignity."
Stephens, in a recent public lecture and an opinion piece in the Guardian newspaper, has called on the IOC to ban the roughly 75 countries -- mostly from Africa, the Caribbean and the Islamic world -- that outlaw homosexual activity. That demand has been embraced by Peter Tatchell, a leading British gay-rights campaigner, and has prompted several human rights organizations to say the IOC should at least speak out, even if a ban at this stage is unrealistic.
"The games would be badly depopulated if you exclude every government with a bad human rights record," said Marianne Mollmann, a policy adviser with Amnesty International. "But we certainly feel the IOC should be more vocal about these issues and bring them up actively with governments where it's clear there are serious violations."
Along with proposing a ban, Stephens has urged still-in-the-closet gay and lesbian athletes to come out during the games, which start July 27. He says those who don't feel safe in their home countries should apply for asylum while in Britain.
IOC spokeswoman Emmanuelle Moreau, asked about the appeals, noted that the Olympic Charter "clearly states that any form of discrimination with regard to a country or a person on grounds of race, religion, politics, gender or otherwise is incompatible with belonging to the Olympic Movement."
Moreau gave no indication if the IOC would do anything to raise the particular issue of anti-gay laws and discrimination among its member nations.
"It's absolute cowardice on the part of the IOC," said John Amaechi, who came out as gay after ending a career in the National Basketball Association.
Amaechi, who is British and now runs a consulting firm there, has been serving on the diversity board of the London Organizing Committee for the Olympic Games. The committee, known as LOCOG, made diversity and inclusion a cornerstone of its bid to host the games.
Amaechi commends LOCOG for seeking to include gays, lesbians and transgender people on its staff, in its volunteer corps and among its small-business contractors. But he's dismayed at the IOC's hesitance to speak out on global gay-rights issues.
"They're abdicating the responsibility that comes with the power they have," he said, drawing a contrast with the IOC's hardline stance in 1964 when it expelled South Africa over its racist apartheid policies.
"Where is that bold, progressive Olympic movement that sees great injustice in the world and says, 'Whatever the risk, we won't let people who violate our tenets join us,' " Amaechi said.
He depicted the IOC executive committee as "a bunch of older, straight men who still giggle when there's mention of sexual orientation."
The gay-rights issue is likely to entangle the IOC long past London.
Russia, host of the 2014 Winter Games in Sochi, has a checkered record on gay rights, and a regional court -- citing a potential threat to Russian society -- has upheld Sochi officials' rejection of a proposed "Pride House" to welcome gays and lesbians at the games.
Advocates, meanwhile, are coalescing around the Olympics in their push for gay rights.
Boris Dittrich, director of the Lesbian, Gay, Bisexual and Transgender Rights Program at Human Rights Watch, said the IOC should be trying to convince individual countries with anti-gay laws that they need to be more tolerant.
"The IOC has been willing to condemn states for their racism, for the exclusion of women athletes," said Jessica Stern of the New York-based International Gay & Lesbian Human Rights Commission. "We have to call on them to take into account the safety and inclusion of LGBT athletes."
Olympics aside, it's an exciting time for gay-rights activists in both Britain and the United States as Prime Minister David Cameron and President Barack Obama each have thrown their support behind efforts to legalize same-sex marriage.
Yet even in those countries, and their Western partners, sports-related prejudice against gays persists. Australian diver Matthew Mitcham, a 2008 gold medalist in Beijing, is one of a tiny group of openly gay athletes expected to compete in London.
Sports leagues in Britain and elsewhere in Europe have been trying to combat anti-gay bias. In North America, there has never been an active player in the top four major league sports -- baseball, football, basketball and hockey -- who's come out as gay.
Jim Buzinski of OutSports.com, which tracks the role of gays in sports, believes progress is being made as more straight athletes support the idea of gays competing openly and as anti-gay slurs become increasingly taboo.
As for the IOC, Buzinski described its current leadership as "a lost cause."
"It's an issue I don't think these people feel comfortable talking about," he said. "It's a group that's going to be one of the last to change."
In London, spectators and athletes likely will glimpse some of the many rainbow-flag gay-pride pins that LOCOG has issued as part of its efforts to show solidarity with the gay community. LOCOG also has touted its efforts to recruit gay and transgender staff and volunteers, and include gay-run businesses among its contractors.
Nonetheless, some British activists are displeased.
Andy Wasley, media manager of the London-based gay rights group Stonewall, said there had been inadequate efforts to launch long-term initiatives aimed at increasing gay and transgender participation in amateur and pro sports.
"Given that the Olympics were won on a legacy of diversity and inclusion, it's striking how little they have done," he said.
He also expressed dismay that out of roughly 550 Britons slated to compete in the Olympics and Paralympics, only two -- both Paralympians -- are openly gay.
Tatchell said he had been meeting frequently with the London organizers to seek an extensive gay and transgender role in the games, and described the results thus far as "a huge disappointment."
One step LOCOG did take was to train its volunteers on dealing with gays and lesbians. A workbook describes a complaint from a spectator made uncomfortable by two men holding hands next to him.
Among multiple-choice answers for volunteers are the options to tell him to "stop being a homophobic idiot" or "politely ask the couple to stop holding hands."
The third answer is: "You explain that there is a huge diversity of people at the London 2012 Games, which includes gay, lesbian and bisexual individuals and couples."