First, one has to figure out what the relationship between sex and nature is. Unfortunately, I could see two answers here, depending on what 'nature' means. Either it means DNA, chromosomes, etc., in which case the relationship is that the latter determines the former (your chromosomes determine your sex); or it's one's nature as a person, in which case it's that the former influences the latter (your sex has an effect on your nature).
based on the remaining analysis, I conclude that the former is intended. Thus, the first sentence means that culture does not entirely determine gender.
Then she says "gender is also the discursive/cultural means by which “sexed nature” or “a natural sex” is produced and established as 'prediscursive,' prior to culture". A simpler version of this is "gender is also the means by which a natural sex is produced as prior to culture". So what this means is that, before culture gets to do its thing, gender produces something. I'm not entirely sure what that something is (what is "a natural sex?") but maybe something like a set of characteristics.
You can put the complexity back in, but it doesn't seem to do much.
Then, she's saying that culture influences this. Also it's politically neutral.
So my translation of her quote is
Culture does not entirely determine gender. Instead, there is a natural way in which gender influences [parts of your behavior that are related to your sex](?), and this happens very early on in people. The culture you're in will impact this further.
Or in a nutshell, she's saying that gender is not entirely a cultural construct. (Is this surprising coming from her?) I'm not sure if this is compatible with it being a social construct.
So I'd say this is utterly terrible writing because it's horrifically complicated when it doesn't need to be, but it's not nonsensical.