SOCHI, Russia—Step out of the main train station in downtown Sochi and most of the people you'll see are volunteers handing out maps. Cross the street and you might also come across three middle-aged Americans handing out religious literature and speaking out against homosexuality.

On Friday evening, while huge crowds made their way to the Olympic opening ceremony viewing party, the men warned that "Judgment is coming" and shook hands with anyone who would stop to listen. A few locals did.

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