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Even when somewhat sympathetic to Natives, white people were still almost always cast as the leads, the Caucasian appearance usually attributed to their being "halfbreeds." The Last of the Mohicans (1920), Hawkeye and the Last of the Mohicans, F-Troop, Iron Eyes Cody's entire career, Broken Arrow, Kings of the Sun, Navajo Joe (Burt Reynolds is a quarter Cherokee), Captain Apache, I Will Fight No More Forever, Sitting Bull, Commanche, Chato's Land, White Comanche, Comanche and Gregg Henry in Body Double all feature white actors playing Native characters.
Redface and negative portrayals of Natives occurred almost unchecked until AIM started staging protests in front of theaters showing anti-Native films. Their efforts (along with revisionist western filmmakers using the genre to subversively attack the war in Vietnam and address civil rights) helped put an end to the universal glamorization of the Native American holocaust.
A couple of important points here. One, that non-Native actors consciously shaded their performances to make Indians seem more savage and uncivilized. Mistakes and stereotypes are what happen when you don't cast roles authentically.
Two, that the practice started to end when Native people protested it. Not when "liberal do-gooders" like me protested it and not when producers decided to cast Natives out of the goodness of their hearts. In case you don't know how the world works, demanding change is usually the prelude to achieving change.
Incidentally, another term for "a movie-going public almost completely unaware of what Natives actually look like" is "besotted fans of non-Native pretty boys who rationalize casting their heartthrobs as Indians."
For more on the subject, see The Best Indian Movies.
Below: "Tell truth. You not know we white man." (An actual quote from the article.)