The Internet makes it easy to dehumanize the other side; they're just avatars and words on your screen. It's a lot harder to hate an actual person, especially just for having a different opinion than you.
[Edited]
But I think your comment is a really good example in and of itself. You've done the binary thinking thing that the article discussed in detail! I've never met anyone who has no problem with abortion, or anyone who has no problem with torture, but I've met people who think the trade-offs justify limited use of one or the other, which I agree or disagree with to varying degrees. It seems likely to me that you're either not talking to people that think these things, and instead building straw-men to knock down, or you're not really hearing the people you're talking to. (Or, I'll admit, it's possible you know a lot more extreme people than I do.)
This article left me more ticked-off than it should have; I think it's because I got the sense that the author valued consensus and national cohesion more than he valued any ideological question. If the article had said, "we're at war, but remember that chivalry is a good thing," I would have simply agreed; instead, he quoted Lincoln.
But on torture? I'm not willing to make any concession to people who think that hanging a Japanese general for waterboarding US soldiers is fine, while leaving a US president entirely unpunished for waterboarding actual and suspected terrorists is not fine. Either we owe the Axis (and especially that general's heirs) some enormous apologies, or we need a few trials of a certain past political administration.
I tend be a fan of bright lines in general. If you don't know that some things are wrong (and, therefore, that any line of reasoning that leads to them has a problem with it somewhere), how do you know when you've gone astray?
You don't have to agree, but people are still worth something and still have valuable information no matter how vehemently you disagree with them.
Also note that the vehemence of disagreement is usually heavily exaggerated, for propaganda purposes. Very few people, in the global sense, are sufficiently different from each other that they're actually totally incapable of getting along. If we make a basic effort to keep an open mind, I think we could fix a lot of our contemporary issues.
A total breakdown in communication and dismissal of people on the other side is not a win. It's a massive loss, one that means that the parent society is on thin ice. We need to maintain basic levels of respect for each other.
(disclosure: I'd ban torture, but for both abortion and most drugs I'd legalise them and try via other methods to reduce the amount that actually occured e.g. better sex-ed and provision of contraception, or better addiction treatment and channeling people towards less harmful (though still currently illegal) drugs.
And the reason why we should be less polarized, politically, is because there are a large number of important issues that can be solved, and need to be solved, even if we can never come to agreement on others. The way politics is being managed in the U.S. is basically an "all or nothing" grab bag on every single issue, with no chance for compromise, and that just leads to hours of pointless rhetoric and gridlock while the problems just get worse.
IMO, one of the parties is a worse offender than the other, but it really only takes one side being intractable to ensure nothing gets done the way the U.S. government is set up.
There's also a video explaining it in terms of funny cat video production: https://www.youtube.com/watch?v=rE3j_RHkqJc
Another take on this, from Scott Alexander: http://slatestarcodex.com/2014/12/17/the-toxoplasma-of-rage/ .
I can imagine quite well that this would easily in yelling at each other etc. Also at least me I even get more hate to views someone says if I talk to him/her personally than when I only have to see his/her arguments in the internet.
In other words: That people of very different views don't talk much to each other is in my opinion both a "self-protection" and quite plausibly rather prevents spreading even more hate.
I find it far easier to depersonalize someone who I don't see in the flesh on a daily basis.
If your only interaction with them is the disagreement, it's far easier to assume they "are stupid" rather than just "have a different opinion."
If you spend 4 hours a day on zerohedge or infowars, you will reach a point where differing opinions piss you off to the point of yelling. If, however, you were getting different perspectives from other human beings on a regular basis, you would likely be less fervent in your views.
It's a lot harder to dismiss actual human beings as "libtards" or "rethugs" or whatever pejorative. You might still disagree, but you usually won't outright dismiss them like you would an article with a "heretical" viewpoint relative to your personal echo chamber.
On the other hand, racial minorities can't really do this: prejudices that exist prior to getting to know somebody have a much easier time both preventing people from interacting as well as having a greater likelihood of persisting during interpersonal interactions.
This is a large portion why the gay rights movement has been progressing at a faster rate than either women's rights or civil rights have in this country.