A few people on this thread have mentioned structural analysis type critiques of gender as something which obtains across both feminism and left-wing thinking and as such tends to mean someone is a lefty as well as a feminist. I think it was Buffy upthread who wondered what the equivalent right-wing analysis might be. I was thinking about that and don't think there is one, as such - because to me more right/libertarian thinking doesn't really go in for Grand Unifying Theories in the same way.
Possibly a digression, but IMO this is probably the most significant difference between the right and the left: the left generally has a vision for society - more just, more fair, more equal etc. It tends towards utopian ideals and has (often conflicting) grand theories about what's impeding utopia and what can be done to achieve it. Conversely, when I think of right-wing thinking I like and respect (and there is lots I don't) it tends to be pragmatic, to have a view of human nature that admits of a level of indelible ugliness as well as great beauty, and to be willing to tolerate a level of conflict and contradiction. Of course the best idealistic thinking may also have these traits, but utopian ideals by definition presume the perfectibility of human nature and as such are more likely to see pragmatism as corruption and human baseness of all kinds as evidence that More Needs To Be Done.
(I should also add that not all utopias are left-wing/progressive utopias, but when I think back over attempts to create utopias throughout history since, say, the French Revolution, the majority of them have been within the broad category of leftist/progressive.)
In that context, I think a lot of modern feminisms are - by virtue of imagining a utopia of gender equality - more likely to lean leftward than not. But as plenty of people have already said, this doesn't necessarily have to be the case. For example a conservative/pragmatic critique I sometimes hear of modern feminist tropes such as 'rape culture' is that while in theory it aims to foster equality and empmowerment, in practice it creates a climate of fear in which the women it hopes to protect come to see themselves as victims constantly under threat. Thus a feminist with a more pragmatic (rather than programmatic) stance might question its effectiveness at actually improving things for women, despite its positive intentions. Similarly, the modern culture of speech codes, 'calling out' and privilege-checking etc is well-intentioned and I absolutely grasp the theory behind it. Its logic is coherent, on its own terms. But personally I question its effectiveness, as a cultural practice, when it comes to actually improving things for any of the minority groups (including women) who come within its ambit.
All of this is to say, I suppose, that it would be a mistake IMO to look for feminist Grand Unifying Theories that have emerged specifically from a right-wing stance. I think this is because those elements of what I consider a right-wing stance that are compatible with feminism (as opposed, say, to right-wing social conservatism, which arguably isn't in any meaningful sense) are generally uncomfortable with Grand Unifying Theories and resistant to the authoritarianism that tends to follow upon trying to realise them in everyday life.