What you describe as the "very privileged white world" sounds exactly how the citizen/police interactions ought to be.
It is a fragile balance that has been built and maintained by your society. The way you describe such as legacy is problematic, as people often see 'privilege' as something 'unfair', something to distance ourselves from. And by saying that the correct citizen/police interactions are a privilege, you push for everyone to average down, rather than make a better world for everyone.
You should instead focus on making sure everyone has the best chance of having a decent civil society. The best start is by using your everyday language as a way to anchor the correct interaction as the goal, not something to be avoided.
Ex:
"Last Friday night two officers brought me to my parents. I was a little too 'agitated'. It scared the shit out of me, but they let me go with a warning. I tell you man, I'm happy to have such friendly officers in my city." (<--- anchor it as a goal)
"My friend from a different place got in trouble with the police last week. It looks like it's a pattern. Hopefully we'll find what is causing this friction soon and stop this shit." (<--- point out it's an unwanted consequence and that something has to change.)