disclaimer: if any of this sounds racist, i'm very sorry its not intentional.
that said...it's always pissed me off to see a person of African decent playing Mimi in Rent (case in point, Melanie Brown) but thats mostly because as a Mexican i wish they'd cut the latin girls out there some slack (bianca marroquin, tho she doesnt look latin) in the broadway world (no pun intended)...
that brings me to my next point - there is practically no such thing as racial purity anymore. you look at me, i look american (from ohio, someone said once) or french, and a bunch of russians mistook me for russian. but i am almost entirely of latin decent (some scottish somewhere i think). same with supposing black is black, white is white, asian asian etc - doesn't work anymore. thomas jefferson had mixed race kids...are you saying that a cultural crossroads such as egypt (invaded by nubians, jews, greeks, romans, abbassids, turks, mongols, and british or french i cant remember - also approximately in that order) is going to have either 100% white or black looking people? doubt it.
the reason disney did this casting is the same reason why they tend to keep the lion king cast as african-american (or canadian or brit or whatever) as possible: there is a really empowering, clear-cut message for black audiences to see a black king on stage on broadway. the KING is black. for the same reason, the nubian princess, the title character, and the heroine of the story should be black. (nubians in general i think did look black, but im not sure). also its important to strike a chord in the american audience: the only significant social struggle in the US being african slaves vs wealthy (white) landowners, racial casting serves as a tool for pathos. in mexico you'd cast the nubians with aztec-looking people and the egyptians with europeans. it can't work both ways because, due to nothing more than history, people of european descent (the conquerors) tend to be on a greater social position than people of aztec or african descent (or conquered), which is why you can't reverse the racial casting. plus the egyptians are the "bad guys" of the story - i doubt that after so much historic baggage, its african-americans the US wants to play this role.
ps. black face is essentially dead. i think they still do it in opera because (face it) opera hasn't evolved much since the end of the 19th century (la boheme).
as for the white chick playing Aida, race is the least of your worries. aside from the fact that purple clashes with red (my theory on the costume change in the second act) you are 14. supposing you have the vocals down, you should concentrate on figuring out what it feels like to rebel against a father (and a nation) for a forbidden (socially, politically, heck - in all senses) affair (not like radames is free terrain) whilst leading her nation in an uneven-sided war and thus facing the death penalty handed out by the one woman in egypt who gave you a break, the one you betrayed - you get my drift...
Tenme por lo que soy, por lo que puedo ser, y si te importo hoy, tenme nena, o vete!