The liberal feminist argument, as I understand it, for legal and political equality was on the basis that if the playing field was level, then it was up to the individual to further themselves.
That's the problem. What does 'further' oneself mean?
I think, first of all, there is a distinction to be drawn between progressivism and liberalism in the postmodern, late capitalist sense. Progressivism concerns the collective struggles, legal reforms and social ideals that you refer to: I would also say it encompasses the labour movement more broadly, as well as the struggles for women's rights and civil rights. Although it originated somewhere in 18th century enlightenment discourse, the great progressive era ran from the reformism of the 19th century - via universal suffrage, colonial emancipation, civil rights - right through to somewhere in the middle of the twentieth century. It is important to note that these movements were predicated on a concept of social justice: their purpose was not to free up the individual to do whatsoever he or she wanted in an open marketplace, but to create a functional and ethical society for all.
To this I would strongly contrast late capitalist liberalism which elevates the rights of the desocialised individual as a supreme value. As you say, the law according to this form of liberalism purely exists to provide a space in which the individual can 'further themselves' within a market system of innumerable choices. This is the Friedmanite neoliberalism which you also refer to: it recognises no concept of society or any value consensus beyond which it's fine to do as you please so long as you don't stop anyone else from doing what they want. In other words, this liberal individualism proposes that the individual should be free to pursue whatever forms legal of self-interest she or he pleases.
It is commonly assumed that neoliberal ideology just suddenly became manifest in the late 1970's, with the rise of the Thatcher and Reagan governments. However I would argue - controversially perhaps - that the advent of neoliberalism was the 1960's, and the people who gave it the most powerful expression were the counter-cultural left. The 1960's and the sexual revolution led to many achievements, but the bourgeoise student left ideal of an individual liberated from normative morals and a dictatorial state is actually exactly the same species of liberalism espoused by Thatcher, Reagan, Friedman and Kieth Joseph twenty years later. It was perfectly natural that so many of the hippies of the 1960's became the capitalist entrepreneurs of the 1980's.
The left that the 1960's birthed were very different from the old left. Here is a very persuasive argument that sexual liberationism was effectively the advocation of a sexual version of the neoliberal free market:
www.abc.net.au/religion/articles/2012/10/10/3607967.htm
Of particular note:
All that said, it is worth noting something very strange at this point. The fight against the patriarchy came to be associated with the removal of social norms that limited freedom in the sexual arena. But doesn't this observation make the sexual revolution sound like the right-wing financial deregulation that preceded the GFC? Or, to ask the question another way, does the sexual revolution lie to the left, or the right?
..though read the whole thing, he's bang on.
Controversially, I would argue that many of the ideologies of the contemporary cultural left - including liberal feminism - ARE projections of neoliberalism.