Sally Haslanger and Ásta Kristjana Sveinsdóttir, ask:
"Is feminist metaphysics just 'mainstream' metaphysics directed at different issues, or is there a deep difference? And if there is a deep difference, what exactly is it?"
Yes, there is a deep difference, and it's one that feminist metaphysics has not yet struck upon, because its metaphysics itself remains traditional and superficial. Feminist metaphysics has not gotten any further than the claim that, in feminist metaphysics, "we're in fact dealing with an ontology of social things, relations, and non-substantive (and often normative) kinds."
But this is merely sociology dressed up as ontology, not a way of thinking truly deserving the title, 'social ontology'. Feminist philosophers are in love with dressed up sociology honoured with the rubric of 'gender studies' in established educational instituions.
The truly subversive rupture in traditional metaphysics in the direction of feminist concerns comes only with genuinely asking the ontological question concerning whoness, and not covering up the phenomenon with mere descriptions of 'social constructs' and the like. Whoness concerns the modes of human beings' presencing in the world. Such presencing in the world AS who you are is indeed marked by a striking duality that, for want of better terminology and only provisionally, can be called masculinity/femininity, which does not correspond to the duality of man/woman.
Presencing in the world AS somewho can be a self-presentation, i.e. a self-presencing, of who you are, or it can be a letting-presence of other whos and whats, i.e. of occurrences of the other. The 'AS' here is the hermeneutic As that is the hallmark of philosophy since Aristotle's announcement in his Metaphysics of an investigation in 'beings insofar AS they are beings' (to\ o)\n v(= o)/n, beings qua beings), the quintessential ontological question: How are beings AS such to be interpreted?
To come to this insight requires a lengthy path of thinking that crucially involves clearing away the debris strewn over the centuries by the metaphysical tradition, that was concerned exclusively with the whatness (quiddity) of things, and never with the whoness (quissity) of human beings. Whoness remained unthought as such throughout, although always implicitly present and even articulated in passing as a matter of course.
Feminist metaphysics is not yet even on this path. It's merely beating sociologically about the bush. And the politics of feminists in their ongoing power plays in academia prevent the question of whoness from emerging to even faintly disturb the all-too-established currents of feminist discourse.
Further reading: 'Metaphysics of Feminism' and 'Was heißt Männlichkeit?' and Phänomenologie der Männlichkeit: kaum ständig noch.