Sociologists may define gender as a social construct, and use the term in that way within their own house; but it doesn't make sense in the real world.

It's absurdly obvious, if you just stop and think about it. The purpose of describing any idea as a "construct" is to emphasize that it isn't real, that it's made up: constructed. Now, in a sense, all ideas, all concepts are constructed, and therefore constructs; the important thing is whether you believe (a) that your idea or "construct" has any relationship with objective reality, or (b) that your idea or "construct" has no relationship with objective reality and can mean whatever you decide it means. Calling gender a "construct," when all ideas are technically constructs, can only be for the purpose of deconstructing it of meaning, i.e., any relationship to objective reality. What the sociologists are saying is that the only meaning "gender" has comes from society, and therefore it can mean anything.

Clearly, many people who say that gender is a "social construct" don't see this; they see only the benefits of not being constrained by objective limits. They think it frees them; but it doesn't.

Now, practically, look at how regarding gender as a "social construct" affects trans people.

If gender isn't objectively real, then being transgender isn't objectively real; there's nothing to trans. So, gender must be objectively real: it must have essence. Otherwise, we are all delusional. A trans person must be a gender essentialist or else invalidate their own transness.

Unfortunately, the sociologists and radical feminists are going to have a hard time admitting these things; they have a lot of skin in the game. They are heavily invested in the "social construct" meme. Ouch for them; their position is fundamentally flawed, and eventually they'll have to face it.