I'm not convinced that most of the "gender is a social construct" people are actually "everything is a social construct" people. A fair number of them like to act like they are; they praise Foucault and Marcuse, they want to "deconstruct" anything that they want to get rid of but have trouble arguing against aboveboard, etc.. But when it gets down to it, this kind of radical postmodernism just isn't how people think. The revealed preference of people is to think and act as if there is an actual objective truth, even if they consciously accept or even proclaim that there's no such thing. For one thing, they have ended up on the side that claims "science is real", and there's a ferocious tension there (even if it's gradually being turned into "we believe unquestioningly in our own declarations of 'the scientific consensus'", which is about as anti-science as you can get save for believing unquestioningly in something that isn't even given lip-service as science).

Anyway, there are lots of things more obvious than that gender isn't purely social. For example, humans--barring accident or developmental disorder--have arms. You wouldn't even think to question whether humans (typically) have arms. Or that rain is wet. Nobody seriously questions whether rain is wet.

For example, a lot of the gender crits ("gender is entirely a social construct") nonetheless maintain that sex is not socially constructed, and that sex-based rights are an important thing--obviously the rights are a social construction, but sex itself is not, in this view. (The trans activists loath this. But the trans activists also aren't very keen on "gender is a social construct".)

Furthermore, when you talk to "gender is socially constructed" types, they are mostly very quick to point out that social constructs are real things that you can observe. They're not saying that there are four lights when there are five--it's more like saying, "I could have put five lights there, and maybe we should." Because the point is to enact some sort of societal change, you can't argue that there isn't even any phenomenon or there wouldn't be anything to change! The question is more tricky: what is the cause of the observed difference?

So it's not clear to me that you're targeting your opposition very precisely to any actual group. There seem to be a variety of perspectives that are getting conflated here, and I don't think that's a good idea, because some of them have some truth to them even if they're overstated to the point of falsehood, and the path to overcoming the falsehoods could be entirely different depending on which perspective you're looking at.

That the far left is happy to try to conflate a number of these perspectives themselves is no more pertinent, I think, than that the right has a historical affinity with the post-truth society itself (and arguably has done at least as much as postmodernists to bring it closer, e.g. https://theweek.com/articles/854892/what-karl-rove-right-about-realitybased-community).

Rather, the thing to do, I think, is insist (1) reality is real, and (2) if someone uses bad arguments, call them on their specific arguments.

The lumping really doesn't help anything, because unlike, say, the idea of Jesus as Savior, "everything is a social construct" isn't really deeply-felt. It's a handy thing to bring out when oppressors say oppressive things like "that's completely contrary to evidence", and put away the rest of the time because it makes life miserable.

(It is useful, however, to counter particular sufficiently well-defined areas of thought, like critical theory. But you can't stop Marcuse by saying "there's a difference between that man and that woman, and it doesn't all go away if the man says his pronouns are she/her and we call her a woman". )