Depends on what we mean by "real". Is it real in biology/nature? No. But social constructs aren't necessarily less real simply because they are social constructs: national borders, nations themselves, etc are all social constructs and they are real insofar as there is a general consensus among human beings that they exist for some meaningful purpose.
The concept of race is a social construct, from the perspective of nature there's no such thing as race because human beings aren't divided into categories, that is, there's no such thing as a "white race" or a "black race" in nature. But as a societal construct it exists as an idea; in and of itself it's not necessarily bad. Where it does become problematic is precisely where the subject of racism comes in:
To regard someone who is different from oneself, on the basis of "race" (which includes, but is not limited to, things like skin color, generalized features, place of origin, nationality, and ethnicity). The 19th century WASP Nativists were racist not only against black people, but also Italians and the Irish.
Racism is a set of ideas, beliefs, etc which regards superficial differences categorized as "race" as a means of justifying views of superiority of ones own group over and against all others; and/or regarding other groups (or even just one group in particular) as inferior. Less overt forms of racism include having assumptions about a group on the basis of race, usually stereotypes, whether negative or benign, such as that Asians are good at math, or that black people are more prone to criminal behavior. Racism can exist as a personal ideology, such as someone who believes that being white is better than being anything else; or it can exist more deeply within societal systems--government, economics, education, etc. Systemic racism occurs when a system is so constructed, whether intentionally or not, as to be favorable toward a particular racial demographic over others. Some of the more obvious and egregious examples in recent history of this include Segregation in the United States, and Apartheid in South Africa. But it doesn't necessarily have to be that explicit to still result in oppression of a group--for example when it's been shown that companies prefer "traditional" "white" sounding names like Mike, Jeff, Bob over less "white" sounding names such as Juan or Jamal. Another example can be seen, in the US, in how disproportionate our justice system is, wherein African American and Hispanic Americans are more likely to face heavier sentencing than European Americans--even for the same crimes.
Disproportionate disadvantages on account of skin color, ethnicity, nationality, place of origin (etc) are examples of systemic racism.
Holding to generalizations and stereotypes based on skin color, ethnicity, nationality, place of origin (etc) are examples of less overt racism.
Adhering to racialist ideologies in which one's own "kind" is regarded as superior than others, or regarding other "kinds" of people inferior are examples of more overt racism.
Recognizing these problems, both as individuals and as a society, is necessary if we want to properly address the continued problems we see in regard to these matters.
While recognizing that "race" does not exist in nature, or as a scientific concept, is helpful; that isn't the entirety of the conversation because it remains a very powerful social construct. Yes, it is perhaps better if we could do away with it as a social construct--but doing away with it as a social construct does not mean ignoring the problems we face today, it means tackling them directly and honestly.
-CryptoLutheran
