I deeply suspect that one reason women don't respect Sarah Palin (among others) is because they think that men don't actually respect Sarah Palin. Here's an interesting clip of Glenn Beck mocking the idea of a Palin-Beck ticket. Feministing argues that Beck concludes it with a sexist remark. In truth, I can't tell whether he's joking about the "get back in the kitchen" schtick or not. But there's a kind of dismissive frat humor that animates the whole bit.
Not that the choices are ever this stark, but I think about Hillary Clinton and how she was relentlessly mocked as a bitch and nutcracker etc. But Clinton, whatever her foibles, was a real, live, credible, threatening politician. I may be projecting, but I think women would much rather hear their heroes mocked because people like Beck think they're ruining America, than because people like Beck don't actually respect them.