Again - you're purposefully making it seem more complex and ambiguous than it is. The "unity" they're talking about is as a group. Effective protests have generally had that quality; I'm sure Vietnam protestors talked about staying unified, as well. It's not 2 different messages.
And I wouldn't say it's just police brutality either. Kaep talked about oppression in general. I think it's a clumsy word to use, but I get the sentiment. I don't think a lot of people really understand what it's like to live in the black community in terms of the relationship to authority, myself included. I heard a guy last night talking about how every parent in that community eventually has to have "the talk" with their kids, and I have heard that a lot over the years. It's a talk white parents aren't familiar with, and do not need to have.