They can hate Sarah Palin all they want, but what they really hate is the fact that they’re not like men, who can have their sex and go their way and not have any consequences for it. They also hate children.
I heard someone analyze this, WRT the beginning of the modern feminist movement.
Women of that time were looking at the immoral behavior of some men, like you said, having sex and moving on without commitment or responsibility.
Instead of requiring men to behave morally and responsibly in order to get sex, these women preferred to figure out a way to act equally immorally.