Anne has a post arguing in favour of a libertarian feminism. It's well worth reading, not least because she's right. But as a persistent contrarian and well-meaning intellectual troll, I want to express some worries, hopefully mixed in with some encouragements, about the project.
To begin with a note of important agreement: libertarians should be more feminist, and should be open to revising their notion of coercion along feminist lines. The NAP is an insufficient framework for understanding oppression, and we should recognise that ideas can contribute towards material coercion even when they are just words. If we can recognise Marxism as a harmful ideology that oppressed the people of the Soviet Union, then we ought to be able to recognise the possibility that patriarchy is a harmful ideology that oppresses women.
Second, she is right that libertarians frequently ignore non-state sources of coercion. This is an accusation which can be made in a number of contexts - nostalgia for the clan systems which states displaced, private crime, etc - but which is not made often enough with regard to the household. The suffering of a citizen compelled to pay the wages of a social worker he will never need to access, while genuine and regrettable, is pretty trivial when compared to the suffering of a woman trapped with an abusive partner. Protesting the former situation while coldly observing that the woman is bearing the consequences of her foolish choice of partner makes it hard for libertarians to be taken seriously by anyone who gives compassion a role in their politics.
My main concern with the libertarian-feminism project is not that these ideologies are incompatible, but that their motivations might be. Libertarianism goes hand-in-hand with methodological individualism, the belief that the primary (perhaps only) actors in society are individual people. This is hardly surprising: if your political theory places great weight upon the choices of the sovereign individual, then you'd better be pretty sure that that individual exists.
By contrast, Marxists view the individual as insignificant when compared to the great movers of history: the economic classes. I'm not going to go into the details of this, not least because I don't know them. These are not the only ways of viewing the world - one might think human behaviour is best explained at the level of communities, of families, of genes, and probably many other levels besides - but they are both popular ways, and they are fundamentally incompatible. Hence individualists struggle to make sense of class conflict, while Marxists view all ideology as ultimately a cover for class interest.
Feminism, it seems to me, has a tendency to view the sexes in much the same way that Marxists view the economic classes. Men collectively oppress women in the same way that the bourgeoisie collectively oppress the proletariat. If Marxism is the attempt to understand the oppression of the proletariat and to unite them for the overthrow of the ruling class, feminism is the attempt to understand the oppression of the female sex and to unite women for the overthrow of men. (This is an exaggeration of most feminists' views, but there was indeed a strain in the 1970s, connected to the Wages for Housework campaign, arguing that the only way for women to escape male oppression is to disassociate from them entirely and adopt lesbianism en masse). They even suffer from the same inconvenience of having to explain why the state, which has hitherto acted only to promote the interests of capital/patriarchy, can suddenly be turned to the advantage of the working class/women.
It's hard for me to tell how far Anne subscribes to this view. For the most part she seems to endorse it: "The sort of radical feminism I’m interested in, and that I see as fitting quite well with libertarianism, sees that society is a patriarchy in which the class of ‘men’ oppress the class of ‘women’." At the same time, she observes that "Women are of course not uniformly oppressed or exclusively victims, and most definitely not a homogenous group with unitary concerns." Perhaps the tension between the positions is smaller than I think, perhaps she has a tension in her views. I don't know.
The picture of feminism I have presented is of course not the only vision of the movement. Intersectional feminism pays a great deal of attention to how different oppressions can interact, and (from my fairly cursory knowledge of feminism) seems like the kind of thing Anne might well be interested in. There are dangers with this view: firstly, that you end up in a kind of "Oppression Olympics" in which different minorities engage in interminable arguments over who has it worst. Secondly, one may ask in what sense this actually remains feminism, rather than merely a "coalition of the oppressed". Such a coalition is unstable, relying as it does upon nebulous judgements about what is oppression and what is merely misfortune (or indeed, self-inflicted harm). It also raises the question of why one cares about the things one does: if your aim is simply to make the world a better place, it seems highly unlikely that this is most effectively achieved by feminist activism. If your aim is to promote the interests of women, it seems equally unlikely that one will achieve this by allying with groups selected for being unsympathetic to mainstream society.
Once again, I don't wish to say that libertarianism and feminism are incompatible. Methodological individualism is compatible with all sorts of theories about why people behave the way they do, including a recognition of the power that ideas, whether or not they are consciously held, can have on society (ctrl-f "idealism"). Patriarchy may just be one such (harmful) idea. But the existence of such a tension may prove a barrier both for libertarians sympathetic to the oppression of women and for feminists leery of relying upon the state for their salvation.