Sure it does. We're a sexually dimorphic species that can only reproduce with one XY and one XX.
Differentiating between them is vital to the continued existence of the species.
Talking with your buddies of the same gender about how you were hanging out alone with one of the opposite was a tribally significant thing in the early days of speech. It still today implies you might be mating! And babies might be forthcoming.
Maybe for some people? Most of my buddies are of the opposite gender, and me hanging out with one of them doesn’t imply anything different to me hanging out with someone of my own gender.
There are definitely people it matters to, I sometimes get tired of the usual remarks and end up awkwardly using "they" or phrasing tricks to try to avoid them
We're sexually dimorphic, but linguistic gender is not based on biological sex, and sex identification is merely one of a literally infinite number of potential bits of information that one may wish to convey with language. The fact that an attractive woman in her reproductive prime is referred to with the same pronouns as your grandmother and the Titanic is indicative of how useful pronouns are for identifying who may be mating.
It reduces ambiguity, increasing narrowing specificity by half the room on average. I suspect that efficiency trade off showed up in so many unrelated languages because it was useful. It didn't get more specific because that wasn't useful enough. Languages evolve too.
Differentiating between them is vital to the continued existence of the species.
Talking with your buddies of the same gender about how you were hanging out alone with one of the opposite was a tribally significant thing in the early days of speech. It still today implies you might be mating! And babies might be forthcoming.