I think the extent of this anti-women mentality is...well, I hesitate to say blown out of proportion, but it is not the beast a lot of people say it is. The people who are genuinely troll-ish towards girls are a tiny minority, and most of that minority is either attempting to be sexist ironically, or being sexist purely for the sake of trolling ANYONE, not women in particular. Take an actual sample of viewpoints and mentalities of people expressing opinions about games, and its genuinely challenging to find a person who espousing the "Fake geek girl" mentality amidst a sea of people decrying that mentality. Even the monsters of this equation are often times not quite as terrible as they are made out to be.
There are DEFINATELY problems with how the community at large treats women, but those problems are not problems that can be solved by burning our flimsiest straw men. They will involve actively demanding a broader variety of games capable addressing issues of gender in more nuanced ways. It will involve actively dissecting common practices of how games are presented, and developers recognizing problems that they had no intentions of including. It will involve taking risks to add content to games that is not proven to make money, and representing women in a way that currently exists as little more then the rare exception. Imagine a world where if every year, if 100 games are released, if just 5 of them had a Alyx Vance, or Jade, Action Reporter? Or a game that sold sexy males as blatantly as others sell sexy women, and asks that I accept THAT as just part of the price for admission to a gaming experience.
I think that you really hit on a great point with how the community is afraid of loseing legitimacy. The whole culture is afraid of the rise of the casual, of the dumbing down of games, of the obsession with graphics, and many have a glimmer of hope in games elevating itself to where it is seen as just as legitimate, is not BETTER, then movies, books, music or the like. Girls represent this threat in a small way (Through a perception of the rise of the casual gamer), but in a much larger way, the fear is that if games are sexist, then suddenly, they are just defective toys. And that's wrong. Games can have plenty of problems and be legitimate. Just because it does something wrong doesn't mean that it doesn't do many other things right.we may not live in an age where people are very positive on self-criticism, but in the long run, it is better to be self-critical. Its better to acknowledge that a bunch of games can represent something sexist, and it doen't mean you have to stop likeing those game. It just means that there are even better games possible if we think around that sexism.