I tend to think about sexism far more in terms of differential treatment of people (as opposed to specific comments - because rude comments people make are rude, regardless of sex).
While I don't like witnessing sexism in general (and will speak up in certain situations), I've always been most interested in figuring out when *I'm* being sexist and trying to work around that. There is a thing called subconcious or hidden bias, where we don't even realize we are acting in a gendered way (e.g., calling women by first names and men by last names in work environments).
To give one example of a bias of mine, I've coached both boys and girls, and I have coached young women. In that role, I am hyper-aware of not being sexist (and that others aren't either). Yet as an athlete, I have an inherent sexist sense that I can't seem to shake. If I see a new guy and a new girl, I know that I feel deep down as though the girl will not be very good until proven otherwise, whereas I give the guy a complete blank slate. While this might be statistically true based on the sports I play, I wish I could give everyone a pure blank slate starting out. Does it really matter? Not really, because I fairly quickly learn to judge people based on how they perform, not their gender or sex. I am not playing professional sports or competing at an elite level now or anything like that, so my general "coaching" nature takes over anyway: everyone should get opportunities, etc. Still, I KNOW that I can't turn on my competitive switch against women the same way I can for competing against men, and I know what I assume to begin with.
So rather than getting upset at the abstract of sexism, I focus on the real ways it affects me and those around me on a regular basis.