Well, to me, the show's Aang looks just as "white" as the movie version.
As CaptainCanada said, that's because that's what your cultural expectations condition you to see.
While that may very well be the reason, I would appreciate it if you wouldn't presume to know what influences my personal opinions. The sentence as typed comes off as arrogant.
Air Nomads as a whole are clearly based on Tibetan Buddhists; the adult Nomads we saw in flashbacks were distinctly Asian in appearance.
I fully agree on both counts. I'm not saying that the character was not intended to appear Asian, just that it is not too obvious to me.
Aang has rounder eyes, but that's a representation of youth in the visual language of animation, not of "whiteness." (The young Zuko and Azula in flashbacks had bigger eyes than they do in their adolescent forms.)
I wasn't necessarily saying Aang appeared fully white to me in the show, but rather that the movie Aang doesn't look much more "white" than the original. I other words, to me, Aang as seen in the movie looks just fine when compared to the original.
I agree though that the actors cast as Sokka and Katara are too "white", at least in regards to going for "authentic" appearances.