So far, Moscow has shown no signs of giving way to outside pressure. Russia's government rejects the view that the anti-gay propaganda law, as well as another law barring adoption of Russian children by gays in any country, are discriminatory.
Minister for Sport Vitaly Mutko, speaking in Moscow Thursday, insisted visitors to Sochi had nothing to fear from the anti-gay propaganda law, which came into force only a few weeks ago.
"I'd like to calm everyone down," he said. "There's a constitution of the Russian Federation apart from this law that guarantees the citizens the right for a private life and guarantees noninterference in private life.
"This law is not designed to violate people's rights no matter what country they are from, whatever their religion or their sexuality. This law is designed to ban the propaganda among minors."
But gay rights campaigners cite the ugly reality of the abuse inflicted on Russia's LGBT citizens, with the authorities apparently turning a blind eye, as a counterpoint to that argument.
Dittrich recalls attending a Gay Pride march in Moscow in which the participants were beaten up by neo-Nazis and others, some of them paid to disrupt the event. "Russian grandmothers there were throwing eggs, there were swearing priests with crosses and hooligans, neo-Nazis," he said. "The Russian police didn't interfere."
When they do, Dittrich added, it's usually to arrest the demonstrators, not their aggressors.
While it's too early really to assess the national impact of the anti-gay propaganda law, Healey said, the debate around it has "mobilized and animated homophobic groups like skinheads and vigilantes who associate themselves with Russian Orthodoxy to actually violently assault and otherwise harm LGBT people physically."
And Human Rights Watch is not just concerned about the impact of the recent legislation on the gay community in Russia.
"Russia is very influential," said Dittrich. "We see these laws are being copied in Africa now." He cites moves made in Uganda, Liberia, Nigeria and Zambia as being of concern, as well as in former Soviet republics like Ukraine and Moldova.
So will all the vodka boycotts and calls for Russia to lose the Winter Olympics have any effect on this rising tide of homophobia?
Maybe, says Healey.
This is because the Olympics carry a special symbolism -- in part because of the role they played in the fight against apartheid. Many Russian businessmen also have large financial interests in the Sochi Games.
"I think the outcry, and the targeting of Sochi, is probably giving the Russian government pause and they are thinking about how to deal with this issue in the longer run," said Healey.
"I hope they are trying to think about the prospects for LGBT citizens in Russia. They have LGBT citizens in Russia and they have to live with them -- they can't really expel them all unless they really want to imitate Nazi Germany."
By contrast, the World Athletics Championships, staged by the International Association of Athletics Federations, start Saturday in Moscow but have not attracted the same level of protest -- despite IAAF president Lamine Diack saying Thursday that Russia's anti-gay laws are "no problem whatsoever."
With the symbolism of the Olympics in mind, some gay athletes insist the Games must go ahead in Sochi.
"I'm fully against a boycott," New Zealand speed skater Blake Skjellerup told CNN. "The Olympics have been very important to me and I know that a lot of people like myself have worked very hard for these Games.