For my own purposes I am going to summarise a line of argument I think is largely drawn from feminist philosophy of science, maybe especially the work of Helen Longino - see here for an early and relatively complete outline of the argument I summarise below. I'm spurred to do this after some internet discussion made me see that I did not have the same understanding as my interlocutors regarding what the most influential strands of feminist philosophy of science have been. If we're going to disagree about feminist philosophy of science, I'd at least like it to be clear what kind of thing I have in mind! So I hope this fosters dialogue.
(Note that I don't claim any originality for this at all, in fact if I am right in my self-understanding then I am just summarising the results of a well known and developed research programme. I will often mention Longino, but she's certainly not the only person to contribute to this. Some of the relevant stuff is discussed here.)
The line of thought I have in mind can be broken down into four components:
(1) Empiricism - ultimately we evaluate scientific research programmes* in light of how well they help us predict the results of observations, experiments, and interventions. (A version of this - `contextual empiricism' - is, for instance, mentioned in the abstract of the Longino book I link above.) This finds its place in this research programme out of two sources - first, the long standing debate in philosophy of science about empiricism in the sciences. Second, the debates in the 80s and 90s among feminist theorists between `postmodern feminism', `standpoint feminism', and `feminist empiricism'. (For some discussion of the relationship between standpoint feminism and feminist empiricism, as well as other matters relevant to this blog post, see here.) While there have been various nuancings and rapproachments over the years, this is a line of argument typically made by people who went with the third of those options, or at least were very sympathetic to the kind of things that pushed people in that direction.
(2) Under-determination - the kind of evidence we can gather in science, and attendant suite of cognitive values like simplicity, explanatory power, etc, does not fully settle which of various options we should choose when we (or any of us individually) face forced choice situations. If we have to decide which theory to adopt (because, say, we have to take some costly action, and which action we shall judge best to take depends on which theory we endorse) then we shall very often run into situations where these purely cognitive virtues leave us with multiple mutually exclusive options that they jointly cannot distinguish between. Likewise, if we find there are persistent anomalies in the data and we have to decide what to revise, abandon, or adopt in response. This is a very well explored idea in philosophy of science quite widely, and there's a nice SEP article here. For a critical overview of its role in feminist philosophy of science in particular, see here.
(3) Pluralism - Suppose one is trying to do as best one can as an inquiring community at predicting the results of observations, experiments, and interventions. Then in bridging the gap between what the cognitive values + evidence can tell us and what you/we end up endorsing, you should allow for a variety of different `bridge principles' or contextually relevant means of responding to the data to flourish and explore their characteristic ways of inquiring. What's more, one should foster the right kind of virtues among the inquirers to ensure they hear each other's case out and generally remain in respectful dialogue despite this diversity in values and circumstances of inquiry. (This can loop back round into a defence of the empiricism, since it might be claimed that among the virtues needed are proper responsive to empirical evidence as an arbiter of disputes.) Longino defends this in broad detail here and also in a more specific set of cases here, and its also generally supported by a host of arguments in social epistemology, some of which I have even contributed to myself.
(4) Feminism - If one is trying to do as best one can as an inquiring community at predicting the results of observations, experiments, and interventions and accepts that one should thereby foster a variety of different styles of science or value-laden methods of overcoming under-determination, then among them are some characteristically feminist virtues or sets of virtues. This kind of case is often made by pointing to concrete instances of some such values making a positive difference in practice (I personally think that this is a-famous-but-under-appreciated-in-philosophy example of this), but is sometimes made by more abstract arguments that there are classes of problems wherein we should reasonably expect the kind of values associated with feminism to do a better job of things - see here for an instance of the latter.
(*What exactly we are evaluating in terms of its empiricist adequacy is itself a matter of a lot of dispute, don't read too much into my opting for research programmes here - I don't think that's a core commitment of this line of thought.)
So following this through from the beginning we have that - we evaluate proposals for science by basically empiricist lights, and accept that we thereby face an under-determination problem. We argue that by those same empiricist lights we will do better as a community to allow for a variety of responses to our evidential situation, and among those admissible modes of response shall be some driven by characteristically feminist virtues.
To be clear, there are tensions in this view. I'll mention two oft-discussed tensions just to illustrate. One might highlight a tension between (1) and (3); it seems like empiricist virtues are picked out as special, but shouldn't they be just one among many of the value systems scientists or philosophers endorse? Or one might wonder how to stop (3) + (4) collapsing into Feyerabendian anarchism (or Neurathian randomisation)? While this whole line of argument must be founded on some tolerance for the community exhibiting contradictory theories and value schemes, feminist philosophers don't tend to want to end up saying that feminist and misogynistic science each have equally valuable things to contribute! But many of the arguments deployed along the way to (3) and (4) seem like they might have that libertine consequence. Is this a bullet to be bit or is there some in principle difference that explains this tension away?
One might also just directly challenge one of the principles - (1) obviously gets challenged very often by folk with metaphysically realist sympathies, but I have even see people deny (2). This latter can be done by saying that we don't so often actually face forced-choice scenarios, and we should be willing to live in sceptical doubt without committing to options wherein cognitivist values don't settle the matter. I think that some of Haack's critiques of feminist philosophy of science amount to this argument, and my read on young Du Bois is that he would have been committed to something like this response to (2). This just to illustrate that even something as well attested to as under-determination can generate some dissent in philosophy.
And so it goes. But without wanting to settle the matter here -- I think I am pretty sympathetic to each of the points in (1)-(4) so I am not neutral either! -- it seems that this is a very prominent strand of feminist philosophy of science, and when we think of the contributions of feminism to theory of science this deserves some pride of place.