It's not a left/right divide, it's a violent/non-violent divide. There've been people across the political spectrum on the violent side, it's not correlated to the left or right.
https://pmc.ncbi.nlm.nih.gov/articles/PMC9335287/
> right-wing actors are significantly more violent than left-wing actors
https://ccjs.umd.edu/feature/umd-led-study-shows-disparities...
> Numbers [of deaths] for right-wing extremist violence are far higher, with numerous high-profile terrorist attacks as well as lower-level assaults, vandalism, and other forms of violence. Since the 9/11 terrorist attacks, far-right extremists have killed 130 people in the United States, more than any other political cause, including jihadists.
https://www.brookings.edu/articles/countering-organized-viol...