With all the claims (some probably true and some probably not) of sexism in people's responses to Sarah Palin, I've been thinking about a common sort-of-intuitive quick test for sexism that I've been seeing a lot lately.
One kind of evidence for a claim that sexism is taking place involves asking whether the same question or comment would be said if it were a man. The idea is that it's sexism if no one would say the same thing of a man in the same position, which means the treatment is purely based on her being a woman. There's one obvious problem with this kind of test. I would be very unlikely to say that my friend John is in the women's room when he goes into a public restroom, but I might easily say it of my wife. That's clearly not sexism, though. So the proper test needs to distinguish between things that would be appropriate to say of a woman that you wouldn't say of a man. The issue then becomes which ways are appropriate to treat women differently from how you treat men. That, of course, is a matter of disagreement between various people, and thus this test is hardly independent of moral views. So measuring sexism this way depends on what your larger moral picture is.
For example, there are those who thinks mothers and fathers generally bring different things to parenting, and thus (other things being equal) they would prefer that if one parent stays home with the kids that it be the mom. Some takes this to the more extreme view that the mom just ought to stay home without the "other things being equal" qualifier. Then there are those who think there's no moral reason to prefer either parent (and I've never met anyone claiming that we should prefer it be men, but that view is logically possible and might well be held by some feminists who seek to equalize men and women in every way).
These views would say very different things about a claim that a woman ought to do what she can to be the stay-home parent. Some will find it sexist, based on their background moral picture. Others will not. I think this is why some people have a hard time recognizing sexism that others see. It's very difficult to find a morally inappropriate expectation when your own moral view actually requires that expectation or at least sees it as worth trying for if other things are equal. (I should say, though, that it's hard to see a typical liberal using this response appropriately against typical conservatives, because typical liberals have a much larger set of things that they consider sexist than the typical conservative does, not the smaller set that this response assumes.)