Well, first, this talk is mostly about gender, which is completely different than race.
If you think about what race really is, it's not what it seems (unlike sex and gender, which have not only a more consistent historical difference, and a stronger biological one as well). Race is more cultural than anything else.
Sure it starts with physical traits, but whether or not you're black, white, or asian, does not depend on your biology. You're actually not born that way (even if the labels make it seem like you belong to a certain geographical location, they're just labels), and the proof is people who are of mixed race.
People who are half black, half white, from my experience, they choose which culture to belong to, and we all confuse it with their race. Obama is a great example. People saying he's our "black" president. What? What does that really mean? He's clearly half white, half black, so why is he a "black president"? That statement is inaccurate, and people should always say, he's our first "half black, half white, president". So what's going on there? People just categorize themselves, and it's just a matter of the stories and memes they adopt from a set of some kind of cultural background. In other words, it's all made up. Half-white, half-black people often choose to be black because they think black is cool. They adopt that culture and roll with it.
So in short, if people keep categorizing themselves, there's no way out of this. Categorization will lead to division among people. "Black" people are just Americans with a different sub-culture, that's it. "Black" people are just as racially diverse among themselves as they are in comparison to "white" people. There are "blacks" from east Africa, west Africa, and Saudi Arabia. Every "black" group is culturally and ethnically different. Why group them?
I'll recognize there is a history to be dealt with here. And that is that we've inherited inequality that is for the most part based on skin color (because that's how our ignorant ancestors decided to categorize people), so that division of inequality still lingers. But there is a case for both repairing the damage, while at the same time getting everyone to forget there is any kind of racial categorization. There is only sub-cultures within American culture.