When Coca-Cola parked its Christmas truck in the central London neighborhood of Covent Garden last month, the soft-drink giant likely thought that some free soda and holiday decorations in a major shopping area would be an easy opportunity to spread a little bit of marketing good cheer in Coke’s direction.

That is not how it worked out.

Gay-rights activists hijacked the celebration. One attempted to climb atop the vehicle, and protesters chanted, “Coca-Cola, shame on you!” while holding up posters that read, “Coca-Cola sponsors anti-gay Russian Winter Olympics. Boycott Coke!”

Scenes like that have been repeated around the globe in recent months, with targets including Coke, McDonald’s and other major multinational corporations sponsoring the upcoming Winter Games in Sochi. Near Chicago, a group of protesters stood in front of McDonald’s headquarters with a banner that read, “McDonald’s: Stop funding homophobia.” Trucks with billboards that said, “Speak out against Russia’s anti-gay laws” circled Coca-Cola’s headquarters in October.

Yet Coca-Cola, the oldest Olympic sponsor, has a good record on gay rights in the United States, said Andre Banks, director of All Out, an LGBT-rights group that has organized many of the protests against Coke. “At the very least, they should speak out, consistently with their own values,” he said.

So far, however, Coke has stayed relatively quiet when it comes to the Sochi Games.

The Olympic Games usually offer a great promotional opportunity for corporate sponsors, as athletic achievement, good-natured international competition and company logos beam to hundreds of millions of TV screens around the world. But this year, Russia’s unsavory human-rights record, especially when it comes to anti-gay legislation and recent homophobic comments by top officials, has threatened to change the focus of the games, leaving the 10 major corporate sponsors in a tough spot.

The primary issue is Russia’s stance on gay rights. In June the Russian parliament passed a Kremlin-backed law banning “propaganda of nontraditional sexual relations,” effectively stigmatizing Russia’s gay community. Putin recently attempted to reassure the critics of the law, saying that LGBT athletes could feel “calm and at ease” but then caused global headlines by adding they should “leave the kids alone, please.”

The inflammatory anti-LGBT law and statements like that have garnered the most attention, but other contentious issues include the withholding of migrant workers’ passports, forcible evictions of Sochi-area residents from their homes and harassment of civil-society groups that speak out about the games. That means Sochi has suddenly become a magnet for protest and controversy.

“The Olympic flame can throw light on the human-rights violations that the authorities would prefer to hide behind the celebratory decorations,” said John Dalhuisen, Amnesty International’s Europe and Central Asia program director, in a recent statement.