I get none of those reactions. BLM are simply asking for equal treatment, not special treatment. Considering the "all lives matter" movement, if you can call it that, is more of a spiteful and petty response to BLM, I'm not sure it's a great example. A movement does not need to devolve into "us v. them" and cause those kind of responses you list. The only reason BLM would be offensive and cause those reactions is if this statement is offensive to your being -- black people having equal rights as white people.
The "black lives matter" movement is a great example of a movement being required because they have been shut out of a "community" that already exists. That community being their actual community they live in. The community is the problem. All those things you have listed -- fear, disgust, resentment, contempt, despair -- are things black people have experienced against them at the hands of our government/police and that is why BLM exists, and that is why a movement is needed to change the community. Just like the civil rights movement, which is not over.
I agree many movements do not have clear goals, but that often speaks to their poor leadership (e.g. occupy wall street), not a problem of movements in general or their grievances. Look at the civil rights movement. I think movements often arrive because the community has failed them.
I would be interesting in hearing more practical examples of how a community would better solve some of these problems (or historical 20th century problems) over a movement, or what that distinction truly is or means. Definitely curious!