Lots of interesting and insightful comments; really glad that there is some debate on this.
My main point would be to be specific - this is not liberalism, it is neoliberalism. Liberalism would certainly support individualism and autonomy; but one of the founding principles is that this should not be at the expense of harm to others. Liberal feminists in particular argued for women's political, legal, educational and employment equality. They did not challenge the biological category of woman - indeed, the arguments were the being a woman and all that entailed biologically should not preclude access to public spaces. They weren't arguing for the abolition of gentlemen's clubs; just access to political, educational and social space where they wished to bring women's issues to bear and provide equal opportunities for women.
Neoliberalism is about identity politics as a market value, which is a different thing. It is about proclaiming diversity, whilst dominant groups continue to obtain their economic and political goals and deny equality and social justice. Neoliberalism does not threaten social structures, it upholds them, particularly as these structures are free market, and not oriented to social justice. Anyone who talks about trans* advocacy as 'liberalism' should be clear that they mean neoliberal identity politics, which dilute and de-politicise gender issues, not bring them to the fore.
Liberal feminists argued for political representation precisely because they thought having the vote and a political voice would help improve maternity care'; access to contraception; access to abortion and so on. Liberals wanted access to power on an equal footing to address maternal mortality; female genital mutilation; gender based feticide; and so on. It is NOT liberal to want to silence women whose experiences are shaped by biology; it is NOT liberal to seek to no-platform biological women, either by disallowing them to speak or by taking the only place they have a representative voice when two LGBT ones are available; that is NOT liberal, it is neoliberal, it is driven by dominant relations of power, and it serves the market.