No, one been male of female is NOT a “social construct”.
I know, e.g., a cat is a male or female — unless they damaged physically, they exhibit different behaviour. And it is not like cats have a “society”.
Whether you personally like it or not, there is a norm, overwhelming majority of people are defined as male or female by their hormones and we are hard-wired to make this distinction.
Yes, some people are born different and some people might become different due to environment. You can be born without a leg or you can loose a leg. It does not make you less human, but it means that the number of legs you have is not a norm for humans.
It is not the right of the rest of us to tell people what they do in their bedrooms. And we, as a society, need to tolerate the differences. The fact that there is a norm does not mean that somehow the norm should be enforced on those who deviate.
If a man fancy wearing a dress — it is fine with me. If he fancies to cut his balls and call himself by a female name, I am OK with it and I will go along with it, calling this person a “lady” and using “she” pronoun.
Just don’t expect people to change what they perceive as a norm or to change their language just because someone who went to do sociology in a University came up with a stupid idea as a result of politically correct indoctrination.
We should all tolerate each other — those representative of the norm to tolerate those who are different and those who are different to tolerate the fact that the rest of the people have a language that is binary in relation to gender.