Twitter outrage mobs (all social media outrage mobs) are manifestations of collective narcissistic rage. Even more or less sane people when united with others are prone to dehumanize themselves and join the yapping dog pack in its mad rush to rip the fox to shreds. The presence of anyone with different opinions or values is enough to set them off and when there’s a spark (and there will always be sparks) they’re off to the races.
They should be dealt with the same way that narcissists should be dealt with (my strategy is to avoid them as much as possible and to be polite and distant and emotionally disengaged when it’s necessary to interact with them).
There is not a single case of apologies helping diffuse a twitter mob’s rage so no effort should be made to listen or interact with them beyond a polite variation of “I don’t care what you think”. In real life, dealing with an enraged narcissist this is not advised (and could lead to violence) but online it’s more than the mob deserves. The optimal strategy is to ignore them and let them rage to each other until they wear themselves out and have to take a collective nap.
Disclaimer: The one and only social media I can identify with at all is Twitter. That doesn’t mean I find it valuable most of the time (it does have its uses). But it’s often amusing; the short format, at its best, is ideal for honing clever one liners and as such it’s a bit like a newer, much, much bigger and meaner Algonguin Round Table (with a bunch of unclever boobs sitting in and getting in the way of the venomous darts flying around and or taking it seriously and harshing everybody’s vibe).