In my opinion invading a private group isn't cool. There are better ways for them to affect the BGS, and support their cause without alienating fellow players. Until there is a way to automatically enforce private group rules there is very little that can happen.
Except call a spade a spade.
I don't think it's to do with the BGS or supporting a cause, just some children being Knobs™.
This is why we can't have nice things.
Z...