I've had this debate with friends a few times: my perspective is that I don't mind as long as race isn't a central part of the character. Like with James Bond, him being a white Englishman with imperialistic overtones is one reason I wouldn't want to see a black Bond. Whereas as far as I can see, Peter Parker's race wouldn't really matter if it changed: the character wouldn't really alter.
I always thought Danny Rand as a mystical martial arts white guy was always part of the innate ridiculousness of the character, especially when it's kind of done "tongue in cheek" like in Matt Fraction's run.