BLM could separate themselves from the rioters further. Stop the tactics that involve harrasment of citizens. They'll be more likely to be sympathetic to your cause. Stop screaming into peoples faces and using a megaphone in their face. It's insulting and demeaning and just makes them want you to go away and diminishes your message.
Don't protest during hours when the rioters are out (after curfews). Make it clear that the rioting is not something you encourage, participate in or embrace. Not shouting burn it down would be a good start because apparently many people take that line literally and are in fact, burning it down.
Setup open public lines of communication where there can be real discussion and discourse. Be open to listening and not shouting down anything that is viewed as not being 100% in lockstep with your thought process. LLISTEN, LISTEN, LISTEN. This applies to anyone despite their views on the matter.