I hear where you're coming from. I think we have a different perception of the argument BLM is making. BLM isn't making the case that not all lives matter. It is making the case that people who say they think all lives matter seem to not be telling the truth, because when black people are killed where people of other races are unharmed there is no outrage. There are so many things suggesting that actually black lives specifically do NOT matter to a lot of people. How could one possibly address that without mentioning race?
At the same time, the actual platform of BLM would help someone like you as much as someone like me. So the platform isn't differentiating by race at all. Even if you don't support the name of the movement, do you support its aims?
RE: Why Poor Whites and Anarchists Should Support Black Lives Matter