Answer by taking a quote from the following article:

"Sympathy for the Devil" is a samba rock song by the Rolling Stones, written by Mick Jagger and Keith Richards. Sung by Jagger, the song refers to the Devil, written in the first-person narrative, recounting atrocities committed throughout the history of humanity as if they were somehow "inspired" (or at least witnessed) by him. Although it has been deemed by some as "a homage", in reality, no admiration (or even sympathy, for that matter) is declared for the Devil in the song -other than his "own" request. It is performed in a rock arrangement with a samba rhythm, first appearing as the opening track on their 1968 album Beggars Banquet.

In an interview with Creem, Jagger said, "[When people started taking us as devil worshippers], I thought it was a really odd thing, because it was only one song, after all. It wasn't like it was a whole album, with lots of occult signs on the back. People seemed to embrace the image so readily, [and] it has carried all the way over into heavy metal bands today. Some people have made a living out of doing this; for example, Jimmy Page."  Of the change in public perception the band experienced after the song's release, Richards said in a 1971 interview with Rolling Stone, "Before, we were just innocent kids out for a good time, they're saying, 'They're evil, they're evil.' Oh, I'm evil, really? So that makes you start thinking about evil... What is evil? Half of it, I don't know how much people think of Mick as the devil or as just a good rock performer or what? There are black magicians who think we are acting as unknown agents of Lucifer and others who think we are Lucifer. Everybody's Lucifer."  Contrary to a widespread misconception, it was "Under My Thumb" and not "Sympathy for the Devil" that the Rolling Stones were performing when Meredith Hunter was killed at the Altamont Free Concert. Rolling Stone magazine's early articles on the incident misreported that the killing took place during "Sympathy for the Devil", but the Stones in fact played "Sympathy for the Devil" earlier in the concert; it was interrupted by a fight and restarted, Jagger commenting, "We're always having--something very funny happens when we start that number." Several other songs were performed before Hunter was killed.

how did the band handle this?
I thought it was a really odd thing, because it was only one song, after all.