So long as BLM excludes 3/4 of the people who get killed by the police, I see no reason they should not be criticized.
In a racist society, people of the same class and different races are treated differently. In police killings, there are a few exceptions of all race to the rule that the police kill poor people, but those exceptions are too few to change the statistics. In police killings, poor white people do not have white privilege.
And because it is hard for people who essentialize race to hear that, I'll add that this does not mean racism is over all things.
But if not being killed by the police is white privilege, then middle-class and upper-class people of color have it, because they are statistically as safe as their white peers.
If criticizing capitalism is soft-pedaling racism, I'm in good company. Du Bois, King, and Malcolm X after he left NOI did that.
Do you think it a coincidence that police killings are linked to poor neighborhoods, that the police primarily interact with poor people, and that the racial statistics of poverty and police killing are identical for black and white people?