As a long time family law practitioner and mediator, I'm often taken by the fact that people who once shared so much wind up being incapable of hearing and processing what the other is saying.
When this happens, I find the cause to inevitably be that one party is completely into rage - sometimes justified but mostly not. The enraged party is of the fervent belief that the rage must be expressed as loudly and frequently as possible to as many people as can hear it, because all those other people are interested and eager to hear about what is enraging the mad.
When this happens, lawyers and mediators understand that we're dealing with crazy emotionalism, and that in order to accomplish something, that emotionalism has to be turned off. My personal preference is to listen quietly for a minute or two, and then say in a dispassionate way "yes, I understand that you're angry, but the reasons for that anger are past. We need to come to a resolution of this issue, and anger isn't going to allow us to do any productive work. What kind of solution do you see?"
At some point, we talk about the counterarguments and concerns of the other party and ask them to consider those, forcing them to express how they believe that those concerns are either unfounded or to come up with something "outside the box" to address those concerned.
Most of the time, domestic cases are resolved, with only the hardest core crazy being unwilling to go through those mediating exercises.
Now, back to the subject of the title - I've been taken by some of the rhetoric I've been hearing, and am reminded a whole lot of really bad divorces. There is a complete inability for disruptors to recognize that the people conducting the meeting might be annoyed with the disruption and the absence of listening on their part. Compounding the problem is the extent of the rage, the chanting, the mob dynamics which completely erase any possibility of any exchange of information or ideas. It becomes impossible to cool a situation when a well-intentioned member of congress is stridently and repeatedly asked about some talk radio/tv fueled talking point, and when they finally get what the inquisitor is asking and respond, are shouted down as "lying".
I will say that given the mob dynamic, there is no easy answer beyond announcing up front that there will be an opportunity for everyone to speak, but disruption by chanting, shouting over speakers and the like will result in the disruptive being ejected. Listen, but then advise that you understand that while they are angry there are people with other concerns, then name them. Talk about recission, talk about job loss, talk about cherry-picking, talk about the expense of COBRA, talk about how large a part of the economy is now entwined in medical care. This time, it isn't so much about the uninsured, it is about the insured and the risk and expense to the insured. Ask how many are on medicare, and whether they would deny others the sort of care they get themselves.
In some purple districts, it will make a difference and tone down the rhetoric, in redder areas (or those which border solid reds), it won't.