I've never seen anything even remotely related to feminism, pop or theoretical (granted, I'm more familiar with the pop manifestation than the theoretical side), which suggests anything other than "women are only x because of culture". That's inextricable from blank slatism.
You're accusing the feminist angle of presenting a false choice, which boils down to either a) constructivism, or b) essentialism. And you're not entirely wrong either, because a good deal of pop feminism does this; or rather, perhaps it appears to because it completely ignores the theoretical subtleties underpinning its own discourse. This is one of the problems I have with leftist discourse presented the political sphere: it usually ignores more complicated theoretical details for the sake of communication. Which is unfortunate, because this actually inhibits communication down the line.
The constructivist claim results in what Judith Butler calls "discursive monism," meaning that everything can be reduced to the effects of discursive interactions (this includes cultural interactions - i.e. "we are x because of culture"). In fact, Butler provided a refutation of the constructivist claim in 1993 when she wrote
Bodies That Matter, but no one pays attention to this text - they go for the more provocative and controversial
Gender Trouble (I think from '87). Critics attacked Butler, after her first book was published, for claiming that gender and sexual identities are reducible to discursive traditions and language games, and for denying the reality of the material body. Butler gives a different version of her method by highlighting the impotency of reducing the debate to a decision between constructivism or essentialism:
Paradoxically, the inquiry into the kind of erasures and exclusions by which the construction of the subject operates is no longer constructivism, but neither is it essentialism. For there is an "outside" to what is constructed by discourse, but this is not an absolute "outside," an ontological thereness that exceeds or counters the boundaries of discourse; as a constitutive "outside," it is that which can only be thought - when it can - in relation to that discourse, at and as its most tenuous borders. The debate between constructivism and essentialism thus misses the point of deconstruction altogether, for the point has never been that "everything is discursively constructed"; that point, when and where it is made, belongs to a kind of discursive monism or linguisticism that refuses the constitutive force of exclusion, erasure, violent foreclosure, abjection and its disruptive return within the very terms of discursive legitimacy.
The terms she's using at the end there are all very poststructuralist, but she's basically saying that material things - bodies and the sexes they have, or perhaps are - play a formative role in what we take to be discursive constructivism, and that this operates in an exclusionary manner. In approximating various identities, bodies are evaluated in a constructivist sense based on how well they achieve their approximation. In an ideal world, every single body would have its own unique identity, which at the moment is not practical (hence, in my opinion, all the online humor circulating about dog-kin, tree-kin, etc.; but even this isn't an escape of exclusionary identity since it merely says that human bodily forms might identify with a different bodily form of an already-established identity). In short, Butler acknowledges that physical bodies play a powerful role in the construction of identity.
For Butler, physical bodies absolutely exist; but all attempts to explain their influence on later manifestations of gender identity (that is, all appeals to biological causes or factors) cannot escape the gravitational tugs of various ideological discourses, be these leftist or rightist:
To "concede" the undeniability of "sex" or its "materiality" is always to concede some version of "sex," some formation of "materiality." Is the discourse in and through which that concession occurs - and yes, that concession invariably does occur - not itself formative of the very phenomenon that it concedes? To claim that discourse is formative is not to claim that it originates, causes, or exhaustively composes that which it concedes; rather, it is to claim that there is no reference to a pure body which is not at the same time a further formation of that body.
In other words, every time we appeal to hormones, or biological differences between men and women, or sexual organs, we aren't appealing to any kind of pre-discursive body. Those appeals are still, in themselves, discursive. This doesn't mean that bodies are entirely constructed by discourse, but merely that no claim, constructivist, essentialist, or otherwise, can peel back the layers and get to the true, pure body. Every theoretical or scientific description contributes to our understanding of what the material body is. The origin, in other words, is hopelessly lost.
Plenty of pop feminists misconstrue or completely ignore the intricacies of materiality, likely because they've only read
Gender Trouble or they simply find it too risky to admit to.