Who says Gates displayed racism? You? Who said Gates automatically assumed the cop was racist because he's white? You?
Let me let you in on a couple of little secrets. I always know when I'm dealing with a sexist, but I never assume I'm dealing with one just because I'm dealing with a man. I know it from tone, code words, gestures, attitude, facial expression, etc. You are not a person of color, and whatever your choices in clothing might indicate, you are not a woman, so though you might feel fit to pass judgement on this, you aren't. You don't know what made Gates believe the cop was a racist, and you don't know that he was wrong in his impression.
The point is, the difference between what you are talking about, and institionalized racism which has always been against people of color and not whites, is the very fact that one of them is institutionalized. If you don't understand the real-life ramifications of that for people of color, then I can't help you.