Some mistakes here. I'll correct them. Thank you for your attention. I got my answer in this question. Here are my friend's ideas that I would like to share with you.
"to the extent that" is a correct expression but it doesn't seem to fit your sentence. "to the extent that" requires an explanation of what extent. For example, in "Sales have fallen badly this year, to the extent that we will have to close some of our shops"*, the clause "we will have to close some of our shops" explains the extent. In your sentence this piece of information is missing. At first I thought you meant "to an extent that doesn’t come naturally" (which roughly means "to an unnatural extent"), but reading your description again I'm not sure.
Also, I don't understand what you mean by "over-occupy the space".
"But to the extent that women doesn’t come naturally in an effort to do precisely" does not make any sense (makes less sense than the original).
Pawpaw TranBut to the extent that doesn’t come naturally, women, in an effort to do precisely = But to the extent that women doesn’t come naturally in an effort to do preciselyNot really, no. Your attempt to paraphrase may actually be less clear than the original sentence. Don't worry about it, though, because this sentence is quite difficult to parse, especially the first phrase, with 'to the extent', which I think should be reworded to clarify its meaning. Here's my idea of what the author was trying to say, even though I'm still not sure of the exact meaning.
But to the extent that doesn’t come naturally, women, in an effort to do precisely what they’ve been told, sometimes will over-occupy the space. =
But in an effort to do precisely what they’ve been told, sometimes women will over-occupy the space. They do this to a degree (extent) that does not come naturally to women. (They do this in a more extreme way than what seems natural to them.)
Context helps a lot.
The person suggests that women do not, by their nature, feel confident being assertive and speaking up. However, they know they should. Because they are not comfortable doing this, they "overdo" it - they may come across as bossy, demanding, and a know-it-all instead of assertive.
Again - this is the speaker's suggestion. This is not my personal view!