Depends on the context.
Suppose you have an underling trying to tell his CEO how to do his job when he has little or no experience in the things he's talking about. That guy, regardless of his color, doesn't know his place. That's the non-racist version.
Now picture a black man who is starting a business in the downtown section of some city that is mostly white. The white store owners around him are constantly talking to each other, predicting his eventual failure because he doesn't "know his place", meaning quite literally that the "place" of a black man is working for a white man rather than for himself. That's the racist version.