My notion of 'casting' is limited to questions of who's right for this film, or that film; and on that level I've no interest in diverse casting. If it should happen to arise that the film is a veritable rainbow of humanity, so be it; but my interest is in what works - on a creative level - for the specific film in question. I would vehemently oppose making a character with any creative reason at all to be a specific ethnicity a different one merely to satisfy some abstract standard of diversity.
Well, sure. Casting, say, John Wayne as Genghis Khan would obviously be wrong. To offer a more hypothetical scenario, casting Laurence Fishburne as the founder of the Ku Klux Klan would be a non-starter.
But when we're talking about, say, the Kingpin or Nick Fury or Felix Leiter, the character isn't defined by a specific ethnicity.
As a practical matter there are enough characters whose ethnicity is simply irrelevant that this isn't a significant impediment to achieving a diverse casting base across the industry, but it does crop up in individual films. I would've liked to have seen Chekov made a woman to address the glaring gender imbalance on the bridge of the nuEnterprise; but only because the character is so much a cipher that one could do almost anything to him - besides making him other than Russian - without treading on toes. Making, say, Spock a woman is an entirely different proposition.
What I find interesting is that the new ST cast is a lot more international than the original. In TOS, the main seven cast members included two Canadians and five Americans, of whom three were the children or grandchildren of Jewish immigrants from Eastern Europe, one was the child of Irish immigrants, one was Asian-American, and one was African-American. In the new cast, you have an Anglo-American, an Irish-Italian American, an Afro-Latin American of Caribbean parentage, a New Zealander of German parentage, an Englishman, a Korean immigrant to America, and a Russian Jewish immigrant to America.
And without commenting on The Last Airbender specifically - because I know almost nothing about it - I find something distasteful about taking an existing work and scrubbing from it all evidence that it originated other than than from the Here and Now and Our Kinds of People; and so harbour a general suspicion of remakes in general, and remakes of foreign works in particular.
Well, first off, the animated series was created by two white guys from the United States, one with an Italian name, one with a Polish name. Second, as I've pointed out many times now, the movie's cast is just as diverse as that of the animated series, if not more so; all the animated characters are various Asian or Native American types, but the movie has Indian, Iranian, Maori, Latina, Asian-American, African-American, and Caucasian actors. Nothing has been "scrubbed," just rearranged.
Also, if we're talking about actual actors as opposed to characters, the majority of the main "Asian" characters in the animated series were voiced by white actors. Of the core cast, only Dante Basco (Zuko), Mako (Iroh in season 1-2), and Jennie Kwan (Suki) were Asian, though there were various supporting roles played by other Asian actors such as Sab Shimono, Brian George, Takayo Fischer, etc., and the Earth King was played by Phil LaMarr, who's African-American.