My take on this: Modern audiences seem incapable of discerning the difference between depicting something and endorsing something. In no way does the film endorse the attitudes of Wayne's character, any more than Moby Dick endorses the obsessive lunacy of Ahab. But both are hugely compelling characters.
What I will say is that other minor details could be considered problematic when viewed through the lens of modern sensibilities. For instance, the way Jeffrey Hunter treats that Commanche "wife" he inadvertently picks up. It's played for laughs. Does it bother me personally? Not really. The film is a product of it's time and I am perfectly capable of watching and enjoying a cinematic classic without demanding it adhere to the attitudes of the day.