Isn't it rather racist to assume that just because a person has dark skin they are going to support BLM? That's like assuming all white folk support the KKK.
Tradition is frequently stronger in the human psyche than reason. Tribalism in all its manifestation is one of the strongest social forces on the planet. People of lower education level historically display insular social and cultural proclivities. They often tend to be acutely focused on things like ethnicity as the key identifiers which bring them a feeling of kinship "us-ness" with others.
Some black people tend to feel that only another black can relate to their personal POV, needs or attitudes. Same for some people from other non-black societies such as Asians, Serbian, Armenians, Sicilians, etc. They seek out and feel stronger kinship to those who have the same or very similar background or attributes - even if those things are superfluous to their character or intelligence.
It's often not a very rational process but derives from what CG Jung called "non-rational cognition" (feelings and intuitions) which emanate mostly from the unconscious. That is why trying to use rational argument to counter such proclivities in others is useless. They did not arrive at their attitude by a rational process and cannot be dissuaded from it by a rational process.
Tribalism is ubiquitous to human culture and sadly supersedes / overrides rational thinking.
Jung demarcated personalities into thinking-types (more inclined to form judgments and opinions based on rational criteria like facts, figures, logic and reason) and feeling-types, (inclined to rely on feelings/intuitions more than rational information or processes to formulate their strong opinions about the world).
Guess which variety many black people who are proponents of the BLM movement fall into?
