The worst response to sexism is of course to brush it off or cheer it on or suggest that it is somehow "over"; let that not be in doubt. But as good as it would feel to go off on a jeremiad about such things, it's likely going to be more productive to focus on what we the non-sociopaths are doing when faced with the depressingly ongoing issue of people treating others based on a few trivial anatomical differences. Like all problems, it persists because the majority of people are not doing enough to combat it, so what could we the majority be doing better? A lot, probably. Because so often our reactions when faced with sexism are a Pogo paradox-style causality loop of inadvertently making the problem worse.
5Not Thinking of It as Your Problem
Sexism is everyone's problem, but many continue to ignore the fact that we are not two separate species and paint it as a women's issue, to the point where you can reliably predict that any given news article about sexism will inevitably talk about how "women are outraged." No, you know who's outraged? Anyone with fucking common sense. The point is not that women and men face equal amounts or extents of prejudice, because we do not -- women objectively have it worse, every day, everywhere, to soul-eating extremes, to the point where some people quite, quite understandably lose their empathy. The point is that discrimination against any group hurts every group, whether it seems like it or not. Many men complain that they're just as beholden to idealized images, that the pressure to be macho is overwhelming and just as bad as what women face, but there'd sure be less pressure to be tough if you weren't defining men as normal and women as a bunch of weaklings that one must therefore appear tougher than.
You can't discuss sexism without first acknowledging that as a culture we define the heterosexual male as normal and everyone else by how different they are from that arbitrary normal, "arbitrary" being the key word. As a great (wo)man once said, if elephants were in charge, we'd all be constantly reminded of our noselessness. If you're room temperature on the gender thermometer, then you've got the pressure of living up to that, and, even worse, if you're not what's normal, you're constantly being reminded of it. Anyone on either side who thinks they have something to lose by redistributing power belongs in the dustbin of history along with their dumbass old-timey predecessors.
Or think of it this way: If you're a dude and it perhaps bothers you that there are a lot of other dudes out there giving you a very bad name, then this is most definitely your problem. That and your shameful noselessness.
4Not Questioning Institutions
Why aren't there more female investment bankers? Maybe it's actually the same reason there aren't more male investment bankers who aren't insufferable alpha males -- because investment banking is a gigantic fly trap for macho assholes and ideally nobody should be doing it. The real question is why are there so many macho assholes, and why do we let them beat the economy like a rented mule? This is of course in no way to suggest that efforts to reduce gender imbalances should cease, because there are going to be people of any gender who want to be investment bankers for whatever reason, and equality means all of them should by God have an equal chance at wasting their lives (and the legal right to be paid maternity/paternity leave to raise their devil spawn). The point is just to illustrate that what men do is automatically seen as desirable, as opposed to maybe asking if maybe something having no women in it maybe means it's maybe bullshit maybe.
The better reaction would be to glorify whatever it is that's actually positive and ensure that as many people as possible get to do it. Investment bankers don't improve the world. Nurses do, though, and we should be glorifying the fuck out of them and paying them eleventy billion dollars a year and saying what can we do about the crisis of not enough men going into nursing (for me personally, it's because I faint at even the DESCRIPTION of blood, but what's your excuse, gents?). We just assume that we should be doing more to include women in all the dominant institutions, and while that's overwhelmingly true MOST of the time and to imply otherwise would be the worst thing ever, it's possibly in some cases the wrong response and at least a missed opportunity to question the value of institutions that may just be clubhouses for the kind of hideous macho greed that has no place elsewhere. There's seldom the consideration that maybe women as a group aren't doing some things because, like most of us, they fucking have better things to do.