I think every event and location is different. After the fact, write up a report, speak with administration, and ask how they would like you to proceed in the future. Any policy needs to be backed by admin anyway. I would say at a minimum to find some way to have an event sponsor present who is responsible for everything that takes place.
Going out onstage in front of a high school audience to stop an inappropriate act may have further consequences with student behavior. Without being in the moment, it's hard to say what I would do. We
screen acts, and they all know our policy, but sometimes students do pull stunts. On a few occasions we've just killed the vocals. Once I killed all of the sound, and made a polite announcement through the monitors only to get off my
stage. Another time a co-worker popped on the talkback mic and apologized when everything ended, saying the band's foul language must have caused a temporary overload - he got some laughs, and the band was so embarrassed they didn't fight it. All of these worked with the audience.
I've seen administrators and teachers walk out onstage and lecture performances, or make a big scene. The crowd gets more unruly, and the problems just get worse. You can write endless referrals, but that doesn't always solve the problem. I have an advantage that I am a teacher and usually the sponsor, so my performers already know how quietly and efficiently I will solve problems after the show.
If it was someone else's show at the
venue, or my techs were working without me, I likely wouldn't interfere unless there was a danger of breaking the law (nudity, maybe?) or damage. I'd still file a report afterwards, and my techs report to me knowing I'll pass information on.