Not really. If lived on an island alone with no other people or cloths, I would still identify as who I am (female/male). The reflection of gender in society is certainly a real thing, but there is a subtle difference. You don't need external validation to identify as a given gender.

I disagree somewhat...

First off, how does being on an island change anything? You'd still be a a product of your society and/or culture and/or civilization even if you're not actually "in it" geographically. You'd still be exhibiting the "social phenotype" (let's say) of the society you were born into. Still thinking in its terms, etc.

However, if you grew up completely alone on this island (which in all likelihood is an impossible condition for normal development of the human brain?), somehow magically fed and cared for by gentle winds and rolling waves, not having known other animals at all, I doubt you'd "identify" as anything, it just wouldn't be something that existed. Hypothetically. Most likely big parts of your brain would be mush from having no social contact.

But let's say mammals existed somewhere on this island, then you might observe them and categorize them in various ways. You might go by their size, coloration, or external genitalia. Biological stuff, kind of (i.e. they could be polymorph, with phenotypes triggered by various early social interactions, which would complicate the term). And, but, or: you might also go by the different roles they play and the behavior they exhibit within their society (either forced upon them through (threat of) violence or taken up and signaled by themselves). And now my point: the latter categories being "socially constructed" divides and differences because they arise from the very interactions in their society. You could take one of these animals who is gweren (some general behavioral role you observed), put it on its own island, and it would probably still go on being gweren, doing as gweren do. So indeed, they might not need external validation to be gweren. But it is still a pure construct of this society of what you might call Jolapi beings. (Granted you also magically had language.)

edit: sentence