The stunts are organized by a western NGO, they are the orphan children of Amnesty International, they are the soundtrack to the al Qaeda assault on Aleppo, which is why President Obama, and the NATO foreign ministers issued a statement about the band within hours of each other. The good news is that the average P*** Riot demo in Moscow rarely exceeds a dozen to two dozen people, most of whom are linked to Amnesty, FEMEN, or public gay encounter groups.
If Justin Bieber or the Rolling Stones suddenly decided to stage an impromptu concert in a public place somewhere in America without a permit, would the authorities ignore it and shrug it off? Doubtful. Even buskers performing in the New York City subway system can't play without formal authorization from the city.
What about taking such a musical performance into a church? If Jennifer Lopez or Madonna just showed up in a place of worship, stripped down to their skivvies and started dancing around the altar, would that fly in any Western democracy? Not likely.
So why,...
They weren't.
Technically, they were tresspassing, which means that any additional crimes committed while tresspassing get bumped up to the next level of severity, usually a felony.