Very many interesting points made by many posters. I'd like to bring in the concept of Maslow's Hierarchy of Needs (for posters unfamiliar with the pyramid, here's a wee linky to a diagram: www.simplypsychology.org/maslow.html). In our society, to attain particularly the top two tiers (of Esteem and Self-Actualisation) requires (often) money, and (especially) time.
There are questions to be asked about what sorts of accomplishments or characteristics will give a person "Esteem" in any given society, and if those sorts of value judgments might, perhaps, be reevaluated. For example, it might be argued (I do not share this point of view) that the question of trans-women in female sport is at best irrelevant, because the whole idea of attaching so much acclaim and monetary potential to who can run the fastest over a short distance is inherently ridiculous, somehow represents "maleness", and should probably be discarded. A problem that quite a few posters have brought up is that as soon as an accomplishment is seen as "female", it goes down in general Esteem. This is a problem!
The other biggy for me is time. To do anything that is challenging well, you need time, to learn, to develop, and to practise. If you want a society where women are able to reach the top in whatever field, you need to have structures that allow them to invest the time. This is (for women and men) more easily done before one has caring or financial responsibilities. Afterwards, it becomes inherently somewhat selfish, because one has to prioritise the art or the science (or the political engagement, etc.) over other commitments at least a good chunk of the time. And historically, this has been much more tolerated of men than of women, and supporting structures (a wife to bear the brunt, a college to live in, etc.) were seen as natural and necessary. So I think that to have equality of opportunity, one would need a society that gives equal opportunity to access support structures, and that is flexible enough in the nature of the support structures to account for differing biological needs.
And just to contradict myself somewhat, I also think that we attach a bit too much "Esteem" to being outstanding in any particular aspect. It should be as acceptable for a male academic (for example) to write a few less papers but to take care of his ageing parents, as for a female academic to spend a bit more time in the lab and expect her children's father to sort out bedtimes.
Like most problems, the right balance in any context is not simple to find, and ideological slogans are a very blunt instrument. In general, I think we've come a long way. I think we're now at a point where further progress requires deep interrogation not just of societies' value systems, but also of practical implementation. It's bound to be a bumpy ride!