Despite what some people may want everyone to believe, it's actually really difficult for people with modern sensibilities to think (and therefore write) like people did during those times. The genuine
belief that people of a different race were little better than beasts of burden is nearly impossible to comprehend. Sure, you can find a lot of people who are still deeply racist, but by and large most people just can't wrap their head around that mindset. Not really
Sure, calling someone a derogative term and getting faux angry about them drinking in the same tent as you is easy enough. But even the single most racist person in the show, within only a matter of months, has largely turned around. If that's proof that the writers don't truly understand how indoctrinated those beliefs were, I don't know what does.
And the fact that the majority of the audience has gone along with it, too, demonstrates it even more.