I think it might be similar to how mass violence worked out in the Reformation. Protestant riots usually would go and smash up Catholic churches and statues due to their iconoclasm. Catholics didn't have similar material targets so they tended to slaughter Protestants when their blood was up.
The racist and nationalistic ideologies associated with the "Right" seem to lend themselves well to murder as there are few material targets for their outrage. The anti-capitalist nature of left wing ideologies means they can satisfy themselves with going after property. Rich people who might be the targets of left wing mobs are also much harder targets (both in terms of protection and identification) than ordinary people of colour.
That is an interesting theory. I could throw out a few others, although I have no idea if they are true:
(1) The biological differences associated with being more right or left-wing may also correlate to how people cope differently with extreme negative life experience. I don't know if any data suggests this, just that it's a conceivable line of inquiry if there is an asymmetry in left/right and how people with terrible life experiences express it.
(2) The medium-term fluctuations in supremacy in left vs right ideology may present different options to upset people depending on who's on top. For instance the left has had significant dominance in the last 10 or so years, so this may cause disenchanted people to see leftist ideation as being the cause of their ills. Whereas previously when the right has been ideologically dominant (in the 80's for instance, or post-9/11) disenchanted people may perhaps have been more prone to identify fascist militarism or religious fundamentalism as being the cause of their ills. One noteworthy point here is that the 'party of the downtrodden' can shift depending on who's getting the shortest end of the stick in society. In the 80's gay people had a bad time of it, for instance, but relative to that have been in a position of dominance (politically) in the past 10 years.
But even these categorical ideas, while perhaps germane, probably do not sufficiencly narrow down how a particular individual ends up being that broken. It might really require knowing a lot of details about their life, their community, family, etc.
