There's no evidence that women are less sexist than men. In fact, all the evidences is that women and men discriminate equally against women:
http://ideas.time.com/2012/10/04/womens-inhumanity-to-women/
Of course, this does show the flaw of trying to judge the gender of a person by how they present themselves online; while on average men and women may show small differences in communication, there are of course many women that communicate in a "men's" manner and v.v.
I love this: so we can fire sexist stereotypes at will, because if we see examples of men or women not fitting the stereotype, it is just a man acting like a woman or a woman acting like a man, so it doesn't count? Or in fact a woman acting like a jerk would be "acting like a man" and therefore reinforce the stereotype of men being jerks?