> The sexism is what made it work.

This is a nonsensical claim and characteristically (for an
engineering-oriented discussion forum) a-historic. The reason for the traditional division of labour between the sexes is rooted in biology: before humanity had worked out (1) how successfully to control female fertility and (2) make birthing an almost risk free process (a process that started about a century ago, and was successfully completed only in the last two decades) a large fraction of women were either pregnant or had recently given birth. Carrying out jobs other than looking after offspring was difficult for them and deeply problematic for society on many dimensions. A lot more can be said on this than I have time for but roughly, it made a lot of sense to give the task of rearing offspring to female and to let men provide, and protect. What you call, with derogatory intent, sexism, are simply the rational sex-based division of labour and the concomitant social expectations that stabilised and on this biological basis.

Recent innovations in medicine and fertility control such as condoms have -- to a certain extent -- made obsolete (some of) these sex-based social expectations. However, social expectations evolve slowly, more slowly than technological progress. Moreover, it is entirely unclear if the new orthodoxy, that it is unanimously better completely to abolish sex-based divisions of labour, and modern society is currently in a fierce struggle over this question.

Marx, in "Preface to the Critique of Political Economy" (1859) claimed
that revolutions occur when technological development has moved so far
ahead of (and hence made obsolete) the social expectations that govern
propery relations, that revolution must occur:

At a certain stage of development, the material productive forces
of society come into conflict with the existing relations of
production or - this merely expresses the same thing in legal
terms - with the property relations within the framework of which
they have operated hitherto. From forms of development of the
productive forces these relations turn into their fetters. Then
begins an era of social revolution. The changes in the economic
foundation lead sooner or later to the transformation of the whole
immense superstructure.

Whether so simplistic a view is tenable (I don't think so) is another
question and I don't want to side-track this discussion. Instead
I want to remix/repurpose the quote:

At a certain stage of development of the contracteption technology,
the division of labour between the sexes come into conflict with
the existing relations between the sexes or - this merely expresses
the same thing in legal terms - with the property and entitlement
relations within the framework of which they have operated
hitherto. From forms of development of the reproductive forces
these relations turn into their fetters. Then begins an era of
sexual revolution. The changes in the socio-sexual foundation lead
sooner or later to the transformation of the whole immense
superstructure.

It is too early to tell how this will play out. On one hand educating women leads to increases in productivity, because skilled workers are so much more productive. Moreover workers who feel (whether correctly or not) feel that they have self-choosen their career paths, their destiny, are also more productive than workers who feel they are herded into a career. Even though women, on average, still work less then men, I think the impact is already felt, and this
would point towards societies without sex-based divisions of labour
winning out. But there is an antithetical tendency which is difficult to
ignore: highly educated, working women don't have children, or have
only few. We already see this clearly when we compare e.g. female academics with that groups with
traditional sex-based labour differentiation (e.g. conservative
religious groups, and societies that are too poor to offer educational
oppertunities and up-to-date fertility control and reproduction
medicine): The latter are vastly outbreeding the former.

It's interesting to see how this will play out in the long run.