First off, in the rest of this post I use the word "gamer." I don't mean that in the more charged way that the word is often used. I consider anyone who plays games as a hobby to be a "gamer," regardless of how much they identify with the broader subculture.
I think an important factor for why these stereotypes about gamers persist, is because many of the more well-rounded gamers hide this aspect of their life. In fact many people in this thread have said that this is precisely what they do.
And don't get me wrong, I definitely sympathize with that. But at the same time, when well-adjusted gamers cover up their association with the hobby, it necessarily means that a lot of the gamers who are openly and loudly showing their association with the hobby are the ones that are giving the subculture a bad name.
Games can become more and more artistic and profound, but if well-adjusted gamers continue to cover up their interest in the hobby, the stigmas regarding it will never go away.
Sure, if I'm meeting a woman for the first time I don't put my gaming on blast. But if the subject ever comes up, I tell her that I keep a game or two in rotation because it's fun and helps me relax. And I don't lie about what games they are either, though instead of saying "I'm playing Nier: Automata" I'll say something like "I'm playing an action game about robots. It's actually pretty interesting," and then I'll talk about some of the game's interesting themes, which I won't go into here because possible spoilers.
The most important thing is that gamers need to be confident about sharing these interests - but not obnoxious. I'm not going to talk to her constantly about Nier and act out my favorite scenes while wearing a 2B t-shirt that I bought at a con. But I will talk about the things I am interested in and why they interest me.
Until gamers as a whole can find that balance between talking openly and honestly about their interests, but not going overboard and making it weird, then the discourse about the culture will continue to revolve around the more problematic segments of the culture. And more importantly, the status quo in the current stigmas and stereotypes will never change.
Also, I think a lot of people in this thread aren't giving non-gamer women enough credit. If you can talk about a game, use that as a jumping-off point for talking about its themes and ideas, and eventually turn that into interesting discussion that she can participate in, then a lot of times she will be onboard and even find it attractive. It's no different than just snuggling and shooting the shit about the meaning of life etc., it's just that a game was the starting point of the convo.
