The problem is they protest shootings of blacks if there's any way to make them look innocent.
An appropriate response if police refuse to even attempt to build trust with the local community. They wanted distrust, and they got it, so...good work on their part.
Trust will not exist so long as race agitators keep preaching hate.
You assume that state authorities are not, themselves, "race agitators who preach hate."
That sound you just heard that was the trap snapping shut.
The notable problem here is that we have a great deal of evidence that, in many cases, state authorities freely and happily preach hate. One need look no further than the current US president for evidence of that. And just in terms of law enforcement, even Ferguson has examples like Ofr. GoFuckYourself, who ended up being the only officer there to be fired for misconduct - sadly, given the DoJ report, numerous federal court findings, and video evidence of the police attacking protestors and journalists.
ANd, of course, looking back through history, we have Jesse Helms, Sen Ben "Pitchfork" Tillman, every single politician behind the Confederacy, Woodrow Wilson, Michael Bloomberg, the various Nazi fetishists and Holocaust deniers currently running for office, Rep. Steve King, Sen. Ted Cruz...this could go on for a very, *very* long time.
I'd consider all of the above vastly more hateful than anyone legitimately connected to Black Lives Matter (as opposed to some who simply grab the mantle on occasion, or who are actually rejected by every such group).
And this is where we get down to the matter. By your own reasoning, the people who are currently seen monitoring anti-police violence groups, are themselves the very "race agitators" that you claim that BLM is. And while you may consider BLM to be a cause for a decline in trust, the simple fact is that this trust has never been established to begin with, and given the extensive history of police as the violent enforcers of segregation throughout the country, they have in fact earned substantial mistrust - one that "mistakes" like those in the OP only serve to reinforce. And so, when we look to many cases of police violence, we find that BLM is entirely correct when they state that the police are working to exonerate murderers - including Freddie Grey, Trayvon Martin (and he was killed by a random lunatic instead of an actual officer), Eric Garner, John Crawford III, and Aiyana Stanley-Jones, as a few of many such examples.