Well, basically a lot of people seem to identify as either left wing or right wing as a political class (at least this is what I have found on the couple of US fora I have frequented,) and express dismissal to the point of caricature, of the philosophies of 'the other side'. The sociology involved is often also affected by class distinctions - another element of 'us and them'.
So people are put into several conceptual boxes, and assumed to engage in group think. Exemplified by opening statements such as "You liberals ..." or "You conservatives ..."
I think what is possible, when engaging in discussion with people of obviously different socio-political philosophies, is the examination and analysis of the case they are making, in a polite and non-confrontational manner, and proceeding from that point to any possible mutual understanding. But it is quite a lot of hard work, often involving compromise of one's own philosophies, and requires a common purpose, and mutual respect, on the part of both people involved.
There will be some things upon which we will never agree, but upon which we can agree to disagree in an agreeable manner. And it is unlikely that such a process of examination and analysis will result in either party altering his viewpoint 180 degrees. But a few degrees here and there may well result in seeing some part of an heretofore invisible philosophy.
I am totally apolitical in the party political sense, but I have my own views - born of my upbringing, education, and environment - as to how society ought to be run for the benefit of the majority of citizens. Those views, while strongly held, are not necessarily set in concrete, and exposure to other, properly articulated points of view may well alter them.
I'm sorry, I'm not very good at this - but does any of this go some way to answering you questions?