For those looking for a more nuanced understanding of this than the eternal American fight about whether "X is/is not racist", go take some of the tests at Harvard's Project Implicit:

https://implicit.harvard.edu/implicit/

When I took them, I was pretty confident that I was, as a well-meaning nerd, beyond any sort of racial bias. I was wrong.

Although I am deeply opposed to racism consciously, various bits of racial bias lurked in my wiring. It's sort of like how even a very smart person can have plenty of dumb ideas or dumb reactions, especially on topics they haven't paid attention to. Since I took those tests, I've been much more aware of those biases, which a) lets me minimize the effects, b) helps me undermine them over time, and c) has made me much better able to see the subtle effects of racial bias generally.