I think the answer to this has been no, females won't go into engineering more no matter how you culturally delegate personality attributes. Consider the sales of the toys and the admissions rates into engineering programs DESPITE the fact that more women are being admitted to university than men [1], and yet still engineering programs are 80-20 male-female[2], despite the gender neutrality motions taking place and the fact that it's no longer the 50s with openly sexist TV commercials and advertisements.
In the 50s women were prohibited from entering engineering programs by policy, so commercials didn't have anything to do with it. It didn't become illegal for engineering programs to discriminate based on gender until the 70s.
If it were natural differences the number would be consistent internationally. Instead, it varies in Western countries from 9% (Luxembourg) to 31% (Iceland) and has been trending consistently upward, albeit slowly, in the US.
Parents not buying gendered clothes or discussing their child's gender until after birth, texts using "she" as often as "he" or occasionally neither at all. Overall there's more of that social push than there ever was (perhaps because there was none at all).
In fact, there's even a school in Sweden that went hardline on this:
All of those things are fantastic but extremely isolated. Some of those things make the news every time they happen. Agendered thinking is pretty marginal.
I will say that it may take another 10-15 years to see the results of these programs, when these kids enter university. The motions are mostly too recent to affect current post-secondary students.
If it were natural differences the number would be consistent internationally. Instead, it varies in Western countries from 9% (Luxembourg) to 31% (Iceland) and has been trending consistently upward, albeit slowly, in the US.