Many folks make a point about racial identity's social construction. Race, they argue, is not real, it is only socially constructed. But social constructions are real. It is no contradiction to say that something is socially constructed and also real.
Perhaps a humble example from the world of baseball will help make the point. Consider the following little catechism:
Are there balls and strikes in the world? Yes.
Are there balls and strikes in nature (if by nature you understand physical reality independent of human actors)? No.
Are balls and strikes socially constructed? Yes.
Are balls and strikes real? Yes.
Do some people get $3.5 million either for producing balls and strikes or for preventing their production? Yes.
So balls and strikes are both socially constructed and real, socially constructed and consequential. The facts about ball and strikes are also real but they can change, as they would, for example, if baseball's rule makers were to vote tomorrow that from now on it's four strikes and you're out.
But that's just the point, someone might object. "Sure the facts of baseball, a human institution that didn't exist until the 19th century, are socially constructed. But scientists are concerned with facts that were there before anyone looked through a microscope. And besides, even if scientific accounts of facts can change, they don't change by majority vote."