If you are going to implement ethnicity realistically, you are going to create racism.
Currently the only "pc" approach to ethnicity is having a skin colour slider, which will either work on a range from pale white to deep black, or with a colour picker, sometimes resulting in ridiculous tans (green, blue, etc) if there isn't any proper sanity checking involved.
Even more so, skin colour is usually just treated as random trivia with no effects whatsoever -- just look at The Sims 2, where you could even have black natural blondes (which, last time I checked, isn't genetically possible).
Implementing ethnicity is inherently racist. Why? It aknowledges differences, i.e. allows for categorisation into races. That's racism.
The problem is whether or not the implementation is also offensive (i.e. whether people will cry "Racists!" or not). There are many movies that manage to be perceived as "not racist" despite aknowledging the effects of people's ethnicities in society and thus being de facto racist. Most of them are not considered offensive, simply because they are well-made and properly balanced (i.e. not discriminating against any portrayed ethnicity).
Doing this with a movie is hard. Especially if you have to keep the money-givers happy and yet stay true to your artistic vision.
Doing this with a game (as of yet) is nearly impossible.
Games, in most societies, are not yet seen in the same light as movies, books or theatre. They are not perceived as something that is an artistic expression or tells a subjective story, but to many they are still just simulators or mere entertainment -- not in the sense that a movie is entertainment, but in the sense that porn or jumping up and down is entertainment.
It would be possible to do it right, or at least in a way that doesn't offend people who aknowledge games as an artform or cultural element, but I honestly doubt Beth cares enough or has the proper talent and aspiration to do it right, or attempt to do it in the first place.
As an afterthought: Of course people will still discriminate based on appearance even after the bombs have fallen. That's how human minds work. We spot differences and we categorise things based on these differences. And if one of those things happens to show certain properties, we assume those properties to be existant in all things of that category -- be it lifeless things or living ones.
It's one of the most basic patterns of human behaviour and can easily be proven and proven again. It was of evolutionary significance (and still is), but it's also one of the reasons we may never be able to archieve that ideal of peace and harmony.
Everyone's different and we tend to assume that those who share SOME of the properties that make them different from us (or others) also share other properties we have not been able to observe yet.
If you're white and a black man steals your car and you have never dealt with people of a different skin colour before, it's only natural to assume (conciously or not) that the next black man you meet will not be trustworthy either.
The good thing about (post-enlightenment) "civilisation" (or rational science) is that it helps overriding that subjective experience. The bad thing about it is that there wouldn't be much left in a post-apocalyptic wasteland.
Of course everyone'd be skeptical of foreigners no matter WHAT they look like as they would simply not meet a lot of people, but if that foreigner also speaks differently, acts differently or looks differently, the skepsis and potential violence (resulting from fear or mere disrespect) can be much greater.
Let's not forget that violence against and exploitation of minorities has nearly always been rationalised (by the wrong-doers) by the assertion that they are not "real humans" in the same way the wrong-doers are -- nearly every large-scale war has always been full of de-humanisation of the enemy (look at the racist propaganda on all sides throughout World War 2 for an obvious example).
Heck, even murderers and criminals are frequently understood as "monsters" out of the subconcious fear that aknowledging their humanity would make their behaviour purely human and thus "normal" (rather than "inhuman" and "monstrous").
My 2 bottle caps.