To be believable, he has to be white. He wouldn't be in the social circles / position he was at the time if black.
If you keep the character living in the 1950s, then I definitely agree with you. However, we now play bond as living 70 years later where blacks are now allowed in those circles.
Why couldn't Harry Potter be a Chinese girl?
I think you may have a point here. While Harry being a girl would be a deal breaker, the color of his skin, like bond, is not relevant to the story itself. However, would the majority of English boys identify as him? Probably not. Same can be said about Bond... would the majority of English man identify as a black Bond? Not as likely. But then again, I bet that if you played a Chinese Harry Potter movie or a Black Bond Movie, people would forget about the race of the actor within the first 20 minutes. That, of course, would happen if the actors behaved as English without the stereotypical racial behaviors. For instance, black actor wouldn't refer to other black men as brothers. And Chinese Harry Potter wouldn't be an overly polite kong foo master.