"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.
"It's very important for the world to show up in Sochi and be united in this issue, to bring light to and start a conversation about what is going on."
U.S. figure skater Johnny Weir, who is married to a Russian-American man, says the flamboyant nature of his sport means that he can make a stance in Sochi.
"I'm quite well known in Russia, so my sheer presence is a big statement against this anti-propaganda law," he told CNN.
Even Obama doesn't think a boycott is a good idea.
"One of the things I'm really looking forward to is maybe some gay and lesbian athletes bringing home the gold or silver or bronze, which would, I think, go a long way in rejecting the kind of attitudes that we're seeing there. And if Russia doesn't have gay or lesbian athletes, then it'll probably make their team weaker," he said.
'I weep anew'
Meanwhile, rights groups and activists are unlikely to let Russia's treatment of its gay community fade from the spotlight.
Some of the most powerful words have come from British actor Stephen Fry, who wrote an open letter to his country's prime minister David Cameron, International Olympic Committee president Jacques Rogge and London 2012 chief Sebastian Coe asking for the Olympics to be taken away from Russia.
Putin, he says, "is making scapegoats of gay people, just as Hitler did Jews. He cannot be allowed to get away with it ... I am gay. I am a Jew. My mother lost over a dozen of her family to Hitler's anti-Semitism.
"Every time in Russia (and it is constantly) a gay teenager is forced into suicide, a lesbian 'correctively' raped, gay men and women beaten to death by neo-Nazi thugs while the Russian police stand idly by, the world is diminished and I for one, weep anew at seeing history repeat itself."