Because it's easy to tell yourself, "McCain had to pick a woman to get the women's vote. They're that dumb, those women." Having rationalized voting for a woman by showing that it's proof that women are dumb, it's easy enough to vote for McCain/Palin.
I won't paint a pretty picture on this---female misogynists are crucial to the anti-feminist cause. Anti-feminism would be nothing without female misogynists, or at least colluders. (Hat tip to Renee for the term.) Women who oppose equality for women come in two major stripes---the ones who accept inferiority and those who think other women are inferior, but they're the exception. If you're the latter, by the way, you get to be in the IWF but if you're the former, you're more in the CWA. Women who accept their inferiority buy into the myth of chivalry. Like K-Lo, they assume that their reward for letting their brains atrophy and denying their own rights will be that Prince Charming will swoop in and save the day. Well, some don't like men very much, but believe that you absolutely need to be on the good side of men to get by in this world, and find it inconceivable that one could be feminist and still get along with men. I'd put Kathleen Parker in this category. She drips with contempt for men, thinks they're all ready to rape a woman given the opportunity, but still thinks women need to shut up and kiss ass to survive.
And then you have the exceptionalists, the Ann Coulters of the world. They really do believe women are inferior, but think that they're the exception to the rule. And they get away with being honorary men, because anti-feminist men need them to sell the anti-feminist cause. Being an exceptionalist anti-feminist woman is not a bad gig---you get paid well to parrot low opinions of women, and you get to feel superior to half the human race. Most exceptionalist anti-feminists tend to stick more to general conservatism, however. The anti-choice movement wasn't very keen on them, because the philosophy of anti-choicers is that every woman, without exception, should make child-bearing her main occupation, without brainy or leadership-oriented things distracting her from being a womb on wheels. If you start allowing that some women are exceptions to the "all women are inferior" rule, then you have to allow that exceptional women should have access to birth control and abortion to be exceptional. Look at childless Ann Coulter---you can't tell me that she is unaware of how not to have a baby.
But grudgingly, anti-choicers are beginning to realize that it's really hard to conceal how blatantly misogynist your mission is if all the leadership is male, and women are only there to beef up the ranks at protests and provide eye candy to male protesters. So now, a few organizations, like Abstinence Clearinghouse, are employing female leadership. I have no doubt that this is less than ideal for conservative men, but it's a practical trade-off---let a few bitches think they're special in order to keep the rest of them down.
The Palin pick is this strategy personified. She's the woman that gets to be at the top, and the rest of us will see our rights swirl down the toilet. Fan-fucking-tastic.
Also, I'll add that I don't see her getting rejected for being a "secret" feminist like Harriet Miers was. I don't think conservative men will like Palin, but they'll accept that her 5 children might mean that she's one of those true believers who tries to get pregnant every time they have sex. Miers, no way. You know she's like Coulter, all about the sex with no babies. (It's worth remembering that a lot of anti-choice men don't think women would really choose marriage and babies if they realistically had other options.)