Also, it's not obvious at all that there's a messaging problem. I get that a bunch of white people don't like the message. But a bunch of white people will dislike anything black people do to push back against a system that harms them.
For decades white people have been telling black activists that they're doing it wrong. And their main cited evidence is that white people are uncomfortable. MLK got a lot of that, and he responded to it here:
https://www.africa.upenn.edu/Articles_Gen/Letter_Birmingham....
I certainly agree that the "Black Lives Matter" slogan makes me, a white person, uncomfortable. But as far as I'm concerned, that's just what it should be doing. If other people are being maltreated by a system that I have the power to change, that shouldn't feel warm and fuzzy.
Sorry? If they want to create political change in a democratic society, it is their job to convince him.
Think about the technology adoption curve, as seen in Crossing the Chasm. It's not the job, or even the goal, of a person creating a new technology to convince everybody. At any moment, a small portion of people are open to changing their minds on a given thing. Mostly, they do what they grew up with, or what the people around them are doing.
The same is generally true socially. Consider this graph:
http://content.gallup.com/origin/gallupinc/GallupSpaces/Prod...
Now subtract the death rate from that graph. If you do, you'll see that a relatively small number of people changed their minds at any given point. Much of the change comes because old bigots died off, taking their retrograde opinions to the grave with them.
So basically, an activist who wants to change minds, like a technology marketer, shouldn't focus their efforts on convincing everybody. Persuasive efforts are best spent on the people who are most ready to change. Which in my experience is generally the person listening carefully, not the guy who runs up to shout, "No, you're doing it all wrong. Do it my way."