The short answer to this question is: Yes. Yes, it is. However, that doesn’t mean it doesn’t have power and impact, and therefore it doesn’t mean we can just ignore it.
The long answer will have to come from a sociologist or whoever it is that studies these sorts of things. But I can try to give a medium answer.
The medium answer: race is, indeed, socially constructed. Not only is it socially constructed, it’s socially constructed intentionally to privilege whiteness and white people. There is no biological support for the concept of race.
However, society—both our natural casual interactions and also the structures and concepts we’ve constructed, like government and laws and race—still have a huge impact and great power in our lives. Further, that great impact applied to groups of people over time can create or enhance differences that were there before.
For example, people from Europe would already be different than people from Africa in some ways—different languages, different religious values, different marital rites, and more. So if you were to take the two groups and throw them into a new country, there would already be some differences between the two, regardless of whether you called their groupings races.
Now, if you were to identify everyone from Africa with a star tattoo, and everyone from Europe with a circle tattoo, and then every new system in your country privileged the people with star tattoos, the gap would widen. Consistently being unable to get enough food or good jobs, being treated unequally by the medical and police systems, textbooks written about how they’re less-than, and many more factors would draw the circle tattoo bearers further away from the star tattoo bearers culturally and relationally.
This is all, of course, without the foundational change that, instead of both groups coming of their own volition, the Europeans were instead captured out of their villages, beaten, bound, crammed into ships where many of them died, and then put into many generations of forced servitude.
We could carry this conversation on for much longer, but the primary point is this: race impacts us today, race impacted our ancestors (which impacts us today), race was involved in the creation of all of our systems of government and law and education and medicine and more, and it continues to be involved (or inappropriately ignored) in most new systems that are created. And that’s un-just.
So, yes. Race is a social construct. And, just like many other social constructs, it can have dire impacts on our lives.