Rehashing the label "postliberal," above:
I have run with many crowds, including the moderately far left when I was young and moderately far right as an adult. When interacting with those groups, I found myself arguing with people that other POV's sometimes had worthwhile things to say.
You will note that the common thread there is "arguing with fanatics." I still do some of that, but mostly I have decided I'm tired of it and leave it to others. Only when I feel I am likely to be the only contrary voice they hear do I leap into the fray now.
I find conservative arguments, as currently defined, more persuasive than liberal ones on most subjects. Caveats: Some conservative issues are of little importance to me; some conservatives are pretty crazy and don't listen; definitions of conservative and liberal change over time - in some cases they reverse, as in free trade and meritocracy.
Culturally, I have comfort with many members of both sides of the spectrum*, but would likely have more natural rapport with liberals - at least the ones of my own generation.
Here's the difference, and why my label carries the implication of rejecting one side rather than being merely neutral: there are evil, doltish, or dangerous-sounding people, with insult brimming from their lips, on both the left and the right. On the right, you find them in comment threads or if you specifically look for them, by using a search engine or monitoring certain groups. On the left, they are prominent and powerful players - they are the mainstream. Many of the liberals I work with - and they are legion - are personally very decent and tolerant with coworkers or with patients who are different from them in some way.
Yet these nice, tolerant people let drop from their lips statements of prejudice and bigotry that would be reason for firing were they focused in another direction - and they do not see this. They are completely unaware.
This scares the pants off me, because it has shown to be so dangerous in history. Many of the people who were most against the slave trade in the early 19th C in England were also the most virulently anti-Catholic and anti-Dissenter, to the point of denial of what we would call basic rights to those groups. (We probably should abandon that framing of Basic Rights in many of our discussions, however, as they would have dumbfounded even our near ancestors. We think them obvious. We are odd in that.) Recently, some Republican congressman was held up for ridicule for statements he made about the most liberal wing of the Democratic Party being communists. I think he deserved that. But such prominent figures as Al Gore, Joe Biden, Jimmy Carter, Barney Frank, and Barack Obama make similar comments all the time - and I haven't even included the issue crusaders such as Al Sharpton, Andrew Sullivan, Michael Moore in that mainstream list. Every few months a Rush Limbaugh or a Glenn Beck becomes a manufactured controversy for saying the same things mainstream liberals say every day.
So in all the back-and-forth of stupidity and crassness and unfairness I see a thread which I find far more dangerous than gun-nuts holing up and daring the feds to come after them or Christianists who want to send abortion law back to the states and think same-sex marriage is not a problem so much as an impossibility: nice people who do not hear their own words or even consider that their well-meant ideas may conceal something worrisome.
I am Postliberal. I remember what it was like to make those assumptions, to feel how nice it was to be one of the good and smart people, and to use facial expressions and tones of voice as if they were logical arguments.
*On reflection, that's a lie. I find everyone irritating.