I am actually torn about this. On the one hand, I understand and value that anonymity (at least, superficially) is big part of what makes the internet great. But on the other hand, I can't help but believe that we'll be in a completely better society if people didn't have a space to vent their rage in some sort of wide-reaching, public arena. Leaving their only recourse for dealing with such rage to be actual manifested "rage/hate/racism/sexism/other-ism", which is pretty darn easy to point out concretely, and to ostracize.
The use of real names on Twitter, Facebook etc doesn't actually stop this, though I presume it moderates it somewhat. (The "secret sympathizers" may be less likely to join the mob.)
I'm not so sure everyone would shut up. Some people are bold wrt their opinions. We might even create more such people..
Then people would eventually ignore the mere threat of repercussions. Now, we'd actually have to attack them, to make the repercussions real - and this is where it starts...
When that happens, we might see a countervailing trend wherein the internet largely turns against that type of behavior—likely via way of directing outrage and shaming towards those who engage in outrage and shaming.
Ideally, the dynamic would be kind of like a snake eating its tail.