Being black is a big part of the character. The character story is that she is a knowingly crazy, incredible well educated, black women raised by white parents. The character would be less interesting if she was white and everything else was the same.
Yes, the character is black. One of her characteristics is that she's black. Her backstory may reflect that.
But how is it a DEFINING characteristic? That's like saying a "big part of Superman's character" is that he's white because he was raised on a farm in the midwest and his story would be different if he were black, therefore if you were dressing up as Superman, using white-face would be something appropriate to do.
How exactly is someone's race "a big part of the character". Think about that for any "white character", like Ned Stark, or Agent Coulson, Walter White, Cyclops, Wolverine, Batman, Jack Bauer, etc.
Is being white a "big part of their character"? Why or why not, and how is this different than Crazy Eyes?