Character is not about hair color or skin color. It's not about costume. It's about how a person acts and thinks and feels and interacts with others. Anyone who says someone isn't the same character just because he has a darker complexion or a less colorful wardrobe is misusing the word "character."
But these characters are based on comic books. Comic books are a visual medium. The visuals quite often define the characters as much as their personalities. The visuals are what make up much of how think of the characters we love.
For example, and putting aside a character's race, you can have slight deviations in the design, but people are going to expect Batman to have a scalloped cape and a cowl with pointy ears. Similarly (as another site noted recently), no matter who plays him (Romero, Nicholson, Ledger), the Joker is going to be a guy with a white face and green hair.
Some of the (typically the main) characters are so iconic we expect them to look a certain way and if you change the race it changes the visuals to the point where it seems like a different character.
Others, yeah, its silly to sweat it. Perry White, in my mind, is a good example.
I guess what I'm saying is that there is no hard and fast rule either way. And fans who take a position either way may just be more visually oriented than some other fans.