I’ve seen several references online to American troops’ marching alongside Russian troops in Moscow’s Red Square on May 9, which the references label “May Day” (for instance, see here).
But that’s a mistake: May Day is May 1, and is a Communist/Socialist/labor holiday, depending on which country you’re in. May 9 is the Russian V-E Day, and celebrates the defeat of the Nazis (the one good thing that the Soviets did help do, of course after helping the Nazis a few years earlier). Say what you will about the propriety of the Americans marching in the Russian V-E Day parade, especially given the current state of the Russian government. But it has nothing to do with May Day.