Unfortunately the fact that BLM does support police accountability is enough for many deplorables to oppose it as a natural reaction.
I think part of the problem is that when you talk about a subject that has a bit of a divide, you tend to ignore that there are two sides. So, typically, a politician will only discuss the part that matters to them, which only addresses part of the audience and completely shuts out the other. For example, imagine if this was part of a speech on increasing police accountability:
"Lately, we've seen a number of events involving law enforcement officials acting outside the purvey of the law and downright disrespecting the badge that they wear. Unfortunately, this has caused a loss of faith and even a sense of fear for the group that is supposed to help us feel safe. For those that are law enforcement or have love ones or friends in law enforcement, this can be extremely troubling for you. As mentioned, these unscrupulous officials have weakened the faith in the badge that you, your loved one or friend put your life on the line to serve. We don't wish to raise accountability to demonize the police. We are looking to help clear the dishonorable and help restore that faith and goodwill."
Now, you could make that a bit better, but I think it gets the point across. The idea is that you spell out the problem, which shows that you understand with the one side. However, you spend a little more time showing empathy toward the other side as they're the ones that need a bit more convincing. Ultimately, you're just showing them that you're not against them, but rather trying to help them.
Although, I'll be frank in that while what I wrote makes a lot of sense, it does have one problem... it reeks of being politically moderate. Unfortunately, while moderates are likely the best politicians to have as they're likely to work with any side, they usually don't pull in voters as well because they fail to pander to any side's strong belief.