I can pretty much discount prevalence and sympathy in that both are differences in extent, not quality; this may reasonably justify a difference in the extent of the output of the function with regards to responsibility, but not in quality.
I think that if you switch from a grouping that is considered oppressed to one that is considered oppressing (ie, women to men, black to white, western to muslim) it often does change the quality, by going from a positive to a negative sentiment. If a black man is kicked when he's down, by a white man, that's seen as a horrible racist act. If a white man is kicked when he is down, by a black man, that is seen as fighting back against the man. If we actually consider all four men as individuals, rather than as members of groups, this difference dissipates.
Personally, I think that the races don't matter here, but rather the context of the act. If a man kicks a woman, I want to know WHY before proclaiming ethical judgement, same as if a woman kicks a man. I don't accept that group identity EVER is more important than context. (Edit: unless the group identity IS context through some tortured attempt to form the context into group identities, and even then they would be equally important, because they would then be the same thing)
Well, you're possibly aware of the video-recorded social experiments (I can find at least 3, see below*) where two actors, one male and one female, argue in public, with one shouting at, harassing and even hitting the other. When it's the male actor being the aggressor, people intervene to criticise the man, express concern for the female victim and offer to report the incident, but when the female actor does exactly the same thing (they switch roles during the experiment) virtually no one intervenes, and in one video, a woman passing by when the female actor is being the aggressor makes a sort of fist pump action and later explains that her silent reaction was 'you go girl!', and in another video people nearby smile and laugh on seeing the woman abusing the man.
Imo, you can't justify those difference in responses ethically, because there were no differences in the behaviour, but you can understand them nonetheless. People are using their internal estimates of probability partly based on actual differences in prevalence and severity (of male abuse) and in some cases no doubt their personal experiences. Those are partly the context, in other words, albeit the wider one, not the individual one. And yes, in these cases, we could say that identity politics or group analysis is not helpful.
And to go back to your point about prevalence and sympathy being differences in extent, I'm not sure we can discount them because of that, because surely when we talk of the differences (the potential double standards) we are talking about differences in extent, in the wider sense. For example it's not that men are always expected to denounce sexual abuse by males or that [insert alternative group] aren't ever asked to denounce [insert appropriate undesirable behaviour] but that the degree of expectation is greater or more widespread in the former.
Instead of offering a comparison to muslims and terrorism, could we offer the closer-to-the-topic example that women are asked much less often to denounce sexual abuse by females? I think we can see there how both (a) prevalence and (b) underdog sympathies might be validly operating. I'm thinking that the 'higher purpose' factor might even also be involved, given that women's fight for gender equality could and in fact probably would in some cases be cited as a higher purpose, albeit in a way which means it might essentially be a version of (b) in this case.
So, whilst in principle or in an ideal world, men would not be asked to denounce sexual abuse by males to a greater extent than women would be asked to denounce sexual abuse by females, there are ways in which the former is arguably more justified in the real world. Iow, to analogise, we can understand why there are more requests for men to denounce sexual abuse by men in the same way that we can understand why there is more need for women's abuse shelters than men's abuse shelters. So while we can see that both (denouncements should be expected), we can also see why the expectations are greater in extent in one case rather than the other. To say otherwise would be to risk equating things which are not equal and to thus apply the wrong emphasis. And while group analysis or identity politics (as it is sometimes disparagingly referred to) can at times be problematical, it is also often useful, indeed necessary, to explain general trends (and aim for general solutions).
Sadly, one downside is that for some or many men, what it means to be a man is sometimes to be seen as part of a group that deserves more suspicion and less sympathy. And not just in the scenarios illustrated here. I can readily think of a few others.
*
https://www.youtube.com/watch?v=u3PgH86OyEM
https://www.bbc.co.uk/bbcthree/article/5d33c36d-cd41-4351-97ed-4516962d5c44
https://www.youtube.com/watch?v=LlFAd4YdQks