The law, passed in late June, has prompted strong calls among Western activists for a boycott of the Winter Olympics, which Russia will host in Sochi early next year.
The intersection of politics and sports can be awkward, as this year's world championships demonstrates. The competition is being held at Luzhniki Stadium, the main venue used for the 1980 Moscow Olympics that the United States boycotted.
Although the athletes at the worlds won't be competing in Sochi, it's the first major sports event hosted by Russia since the law was passed. It's also seen as an informal test event for the Olympics.
Russia will also host the swimming world championships in 2015 and the World Cup in 2018, so how the law is enforced will likely be a long-standing issue for sports.
Some of the competitors in the Russian capital say athletes shouldn't be used as pawns and it should be up to their individual consciences whether to protest or boycott.
"If the athletes want to do it, that's fine. If the politicians tell them to, that's different," New Zealand distance runner Zane Robertson said. "We don't do this for the politics."
But at least one finds his conscience muffled by the Russian law, which says foreigners can be jailed for up to 15 days and deported for violations.
"I can't talk about it," said American runner Nick Symmonds, noted for usually being outspoken on social issues. "You're not allowed to talk about it here. I'll get put in jail for it."
In a blog entry for Runner's World, written before arriving in Moscow and winning a silver medal in the 800 metres, Symmonds stated his support for gay rights and said, "If I am placed in a race with a Russian athlete, I will shake his hand, thank him for his country's generous hospitality, and then, after kicking his (butt) in the race, silently dedicate the win to my gay and lesbian friends back home. Upon my return, I will then continue to fight for their rights in my beloved democratic union."
Symmonds' concern about jail underlines how the law's vagueness makes it intimidating. The law's definition of "propaganda" hinges on intent. Anyone who distributes information with the "intention" of persuading minors that nontraditional sexual relationships are "attractive" or "interesting," or even "socially equivalent to traditional relationships" could be accused of breaking the law.
Russia has given contradictory signals on how the law will apply to the Olympics. Some said the law would be suspended during the games, but the Interior Ministry has said it would be enforced. International Olympic Committee President Jacques Rogge said last week that the Russian government provided written reassurances about the law, but that more clarity was needed. FIFA has also asked for "clarification and more details."
During the Olympics, the IOC bans athletes from making political statements. At the worlds, two-time world champion Bernard Lagat doesn't appear to have a problem with that approach, preferring to concentrate on his running instead of the controversy.
"I'm happy to answer all those questions when I get home," said Lagat, who qualified for the final of the men's 5,000. "But here I want to focus on the things I need to do."
AP Sports Writer Pat Graham contributed to this report.