Most of the time, yes. At least there are some who find Scarlett Johansson named as Motoko from Ghost in the Shell a problem. Changing her race would change how she would see the world thus create an entirely different story with possibly differen themes.
I may accept this may be a non-case in comic books because it is mostly just "American" culture.
Oh, and this change is only "unacceptable" because it doesn't make sense. Why not make her a cat? Or a can of soda? It is not consistent with that universe's internal logic (no indication that their Japan has natives with European ethnicity). It has nothing whatsoever to do with race. Changing the character to be chubby, for example, would be perfectly fine, as it would not conflict with the world's logic. So not an instructive example.