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I don't think terms like white and black are very productive. Skin color is simply an adaptation to varying degrees of UV exposure in different parts of the world. A person from India, Africa, and South America may have the same skin tone, but are they all "black?" No, only the African is considered black. Ok, then why not just call that person a Ugandan or Moroccan or wherever else they originate from? We should be grouping people based on ethnic and cultural decent.
The thing is, there are inherent morphologic differences between humans depending on which region of the world they originate from, and skin color is just one of those features. We don't really talk about all the other ways that human beings differ in terms of appearance. Why? Because skin color is easiest to identify and describe. But thats about it...its purely out of convenience. At the end of the day skin tone is a crude and fairly useless way to categorize people.
Black and white are terms that stem from racist ideology and should be rooted out.
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As I understand it, the notion of whiteness as a point of study is understanding how societies have conceptualized race, what constituted being white over time, and whatever status/privileges went along with it - namely in the United States. 
And American society hasn't actually been shy on the topic either for quite some time. Statehouses and courts have proven to be happy to weigh in on the matter. Its been not only a matter of social and cultural importance, but even legal. If the topic wasn't taboo for legislatures and courts for centuries, universities should be fine. 
Anyway, the problematic parts you're talking about aren't all that different than any other student being obnoxious after learning something in school. Psych students think they've got the human condition figured out, guy reads Das Kapital and suddenly knows more than modern economists. That doesn't mean its a net negative to try and understand these topics more. 
Where these people are going wrong is they're taking a field of study meant to explore cultural phenomena over decades and pointing fingers at individuals. Not good. 
Anyway as far as social constructs go, it's been pretty damn influential throughout history.  I think it's fair to at least explore the concept as a matter or inquiry.