A "Western" that treated cowboys and Indians in a non-stereotypical or non-racist way probably would be considered a period drama, not a "Western."
I don't know what you are taking about. There are many "Westerns" that don't even deal with "cowboys and indians." What is "racist" about High Noon, Shane, The Ox-Bow Incident, My Darling Clementine, Wagon Master, 3:10 to Yuma, Winchester 73, The Magnificent Seven, Butch Cassidy and the Sundance Kid, True Grit, The Professionals, Ride the High Country, The Wild Bunch, McCabe & Mrs. Miller, The Shootist
or the Man With No Name movies (just of the top of my head)?
This may be a path already started by Deadwood, but I haven't seen any of that. The thing about period dramas is that there's lots of periods to pick from.
"Started" by Deadwood
(1948) not only presented Native Americans as honorable and unfairly treated, but questioned the whole myth of the "taming" of the continent. It also included a Mexican-American character as probably the sharpest and most professional soldier in the picture.
(1948) doesn't deal much with Indians, but does include the Indian character Quo, who is not "savage" but too sharp to be simple comic relief as he trades barbs with Walter Brennan. It's a precursor of the role Chief Dan George plays in The Outlaw Josey Wales.
has already been commented on above. It may damn Ethan Edwards' obsessiveness more than it does his racism, but it clearly shows that Ethan's distrust of the mixed-race Martin Pawley is misguided. It also shows the Indians sympathetically in their winter dependence on the reservation for food and the helpful character of Look, not as simple family-killing objects of revenge.
I will not even comment on '60s and later Westerns, as the revision of Hollywood's depiction of Native Americans was so firmly in place by then it doesn't really need reviewing by me.