I suppose this is the key. No group will be convinced by being publicly ostracised or relentlessly attacked; that's going to do nothing but further entrench division. But it's difficult to figure out steps that one can take as an individual to help.
There are plenty of behaviors that people, specially young people going through the "rebellious" phase of their lives, engage for the shock value, for the "I'm the only sane man among sheeps" feeling and that can usually be explained by the lack of maturity and contact with the real world.
The only result that comes with ostracizing these people is to throw them at the arms of the only groups that will accept them with open arms: people seriously sharing the same ideology and that will welcome this person with open arms.
The real solution to ignorance is not to cut the ignorant from the flock but to show them the errors on their ways.
People tend to grow out of these phases and helping them out in that path instead of cutting them and punishing them is a much better way to deal with this problem.
I first saw it with gamergate a while back. As someone very close to the games industry, and in games media back then, I was very interested by the movement (which, at the time anyway, wanted to put a spotlight on corruption in games media)... then after it did some good, it turned into a "hunt all the SJWs" parody of itself and very much became an example of what the alt-right is today.
What happened there was simply people not listening... and instead of listening, sharing whatever story fell in line with the narrative. Twitter makes it easy to block dissenting opinions. Reddit naturally silences disagreement with downvotes. Facebook just natively doesn't show you the stuff you don't like. Social media is a fucking scourge, I swear.
As the movement becomes more and more extreme, it attracts more and more extreme people and the moderates naturally leave (or convert), as they have no way to fight the trend back on a platform that amplifies the majority.
And of course both "sides" in a fight become involved in a cherry-picking fight of who can find the worst of the other's community and showcase it as proof of how relentlessly EVIL the "other side" is. Because, you know, everybody's like that, right?
It's fucking impossible to be a moderate nowadays. This is probably the main reason why I enjoy commenting on HN, where discussion is possible (probably because of details such as upvote counts not showing and a really nice sorting algorithm). Though it has its own issues with community flagging - Take this post for example: https://news.ycombinator.com/item?id=12977633 (A moderate article that looked at issues on the left, flagged out despite 100+ upvotes)
Outrage is the only reasonable first response to what happened and must come first. If that opens the doors of discussion like it did here, great. Most likely it won't as most people are not persuaded by argument, though they are susceptible to manipulation by sympathy.
When those people choose hate over everything else, however, they deserve to be ostracized and relentlessly attacked. Hate is NOT acceptable. I'm disgusted by those who suggest otherwise, especially in the name of "understanding" the other side. It not only shows an incredible lack of understanding about the human condition, it encourages the acceptance of that hate as a legitimate part of the political process, and brings into question the morals of the person making the suggestion to acquiesce to hate.
Unfortunately, any sort of hate group's views are damaging to society as a whole, and the larger community has to balance understanding and tolerance (with the aim of eventual conversion) with the need to immediately condemn it. I view it as a societal disease that must be curbed.
Sometimes I worry that too much understanding is as bad as none at all. Supremacy of one group of living things over another (including animals vs humans) simply cannot be legitimized to any extent.
I find that people who have racist beliefs often see differing viewpoints as the enemy - the first breach being simple consideration of a new perspective.
I suggest to my left-leaning friends that government should be a "last resort" solution at best, and is frequently actually the problem; to my right-leaning friends I explain the crucial importance of privacy, civil liberties, and equal justice; and in either case the response is frequently incredulous disbelief and contempt for my naivete and/or obvious privilege yada yada yada.
The echo chambers are real, and they are a threat to our civil society.