In the real world making that expression at someone is pretty rude. While it doesn’t enrage me when someone uses it here it doesn’t exactly endear them to me when they use it in reply to something I wrote. (Yeah, invitation for everyone to use it here in this thread. Go ahead.)
In spite of what I just typed there are times when rolling your eyes and sighing are appropriate responses. Honestly, from the article it looks like the eye roller in question is on the opposite side of some council members and they just wanted a reason to eject her.
I imagine it would have to be one hell of an eye roll/sigh combo to meet the requirements of disorderly conduct.
I remember a scene in the sci-fi classic Robot Jox where Achilles (the last surviving member on an older team of American jox) gave this gesture to Alexander (the last surviving member of the Russian team) during some meeting. Alexander (in classic 80’s hollywood Russian style) proceeded to try and tear his way across the room like an angry bull, with everybody holding him back.
At the time, I figured the insult was that Achilles seemed to do the gesture with his middle finger. Maybe they were going for an added subtle insult gesture on top of the obvious one?