Most people like to pride themselves in how tolerant that they are in regards to other people and their viewpoints. Of course, not too surprisingly, those that self-evaluate have a tendency to give themselves a relatively high score, whereas when it comes to others, especially those others with opposing viewpoints, they are often viewed as being intolerant. While it is true, that each of us is entitled to our own viewpoint, it isn't healthy, to just surround ourselves only with people that agree wholeheartedly with what we are saying or doing, because a valued part of life is challenging and investigating our own treasured viewpoints, even points of view of long standing, to see how sound such is, when truly tested, whether such testing is done internally or externally, because in that manner we grow and learn.
One of the most dangerous aspects of groupthink is how intolerant some influential people are within that particular group, so that, when it comes to actually hearing or reading about an opposing viewpoint, such is the perceived threat, that those in power, will not even consider hearing or discussing such, and any within that group that challenges that conventional viewpoint, is considered to be on the verge of being an outcast, or being banned, or being punished, for having the audacity to even consider that there is another side, worthy of consideration or listening to.
The main reason why those engaging in groupthink will not tolerate dissent within their group, is that they cannot afford to have any cracks within their machine, especially internal cracks, because such may weaken the group as a whole, and that weakness, is something that they perceive, would be exploitable by the opposing side, and lead to the very fracturing of the group, and thereupon its groupthink. That is why, so often those that preach that we should have tolerance and respect for the other side, as we would want them to have with our side, are immediately silenced and dealt with forthrightly, because the line has already been drawn in the sand, and dissent of any sort, crosses that line.
Therefore, because of groupthink, neither side is able to come to an accommodating agreement with the other, because neither side, believes that there is a middle ground between one another or will overtly admit to such, even though, there may well be. So too, because of the fear factor within the group, even a minority within groupthink, can effectively control the group, because when internal dissent is summarily punished to the degree that those contemplating such, recognize that to do so, could conceivably cost them their livelihood, their home, and their safety, they will often sacrifice their tolerance of others, for the perceived safety of the group that they are a part of.
People and groups that aren't willing to at least occasionally listen to the other side espouse their viewpoint in a respectful and considerate fashion have traded common civility and common sense, for the pride of selfishness, that will not broker any dissent or opposition, whatsoever. What this does, in effect, is create divisions between people, in which, there is little hope of reconciliation, because neither the people or those groups, are willing to concede that they don't already know everything that there is to know, and that therefore the other side is wrong and ignorant, even though, it is possible, even probable, that the truth lies somewhere in the middle.