I think you're incorrect, Tom. 
BLM is not an inherently left or right-wing group. The only thing that makes BLM a left-wing group by default is that some folks on the right have decided to make it their personal bogey-man. 
The fact is there are lots of very conservative GOP African Americans that support BLM.
BLM is response to police violence and the systematic racism that exists in our society against African Americans, period. Left wing blacks and right wing blacks both have come out in support of the movement (as well as LOTS of people from other communities, even a few right wing white people).  
I am not saying BLM hasn't gotten violent. I am saying you can't toss them in with the left so easily. 
PS I come from a Republican family and three members of my family resigned from the GOP last week over Trump defending Nazi's and the KKK. That is how seriously they take racism and, for the record? My entire GOP family rather sides with BLM as well. Just sayin. 
Be well and take care