We have almost 6,000 people in my city, and two cops on duty in each 12hr shift. We dealt with mentally ill people constantly. So, you're idea of white privilege, and extremely unlikely doesn't make much sense. I've dealt with black and white people, and never shot either. Black mentally ill person charges me with a bat, I din't shoot him. Drug dealer, black guy, has a gun to my head, we wrestled him down, arrested him, no shooting involved. Domestic dispute, black guy, black women, guy runs out with a sword and an axe, within swinging distance, I don't shoot him either. We had a few people that we routinely had to deal with. You become familiar with people rather quick in that line of work. I've probably been to 90% of the houses in my city for one reason or another.
Those I mentioned, I've been involved with them for years and know them pretty well. Even being out of law enforcement, I see them and talk with them.