That may be true, but it doesn't mean a group (as cited Black Lives Matter as an example) then can ignore that "common" circumstance entirely. I don't think the majority thinks that Black Lives Matter can't get what they want because, in the past, they have propped up criminals as heroes or martyrs. When that argument is brought up, it is faced with backlash, rather than a response such as "yeah we are trying to work on that and here are some other things we are doing." However, even this isn't (seen as being) true and it is the fault of media reporting. People in that movement (at least in this area) do have those discussions and are not so quick to react to such statements, nor shift away and then go blame something else. The real leaders of these groups are well aware of the crime issue, the education issue, and whatever else because they are living in those communities and do try to make things work out.
And those leaders are not the ones who get the retweets, post articles on Buzzfeed and "The Root" or end up on the TV news shows.
A lot of the stress people seem to be having over these issues is due to blowhards on the internet.
So you're saying that if the blowhards didn't have their voices amplified, that the message of BLM would be pallatable?