But the police situation is fundamentally a lot simpler than the workplace one, because it is a single interaction. If you fear you are being lumped into a category by them that it is not good to belong to, you really have only two goals:
1. Avoid truly terrible outcomes (being shot, beaten, framed for a crime, etc.).
2. Get re-categorized.
There are many stories in the news of people of color failing to achieve these goals, even when they are pleasant and polite. But there are few stories of pleasant, polite interaction making their situations WORSE ... except that if your politeness is ignored, it can be dangerous to repeat yourself, because that can indeed be construed as a challenge.