I am sexist so yes, I do think there are inherent differences between male and female and it affects everything you have mentioned.

Office politics exists whether gendered or not, but there are certain things you can expect from males and certain things from females, in average. I prefer the male approach to things, it is more productive and less damaging to the company. I could give anecdotes but that's not the point since it is only anecdotes. There are certain things that are just nature, from period to birth to hormonal differences between male and female which affect how things done and the value of the employee.

People claim that the diversity of it all is what makes a business successful, I don't buy this approach because it is evident that most successful and innovative things were created by males, the burden of prove is on the females to push and bring the one opposite example, not anecdotal but something substantial. You and your friends could be the first, but until you make it I will still be doubtful. You could argue that people like me hinder you from achieving things but I don't buy it, in the tech industry where open source exists and where all you need is a computer there are no excuses.

What people care about does matter because it affect the way they work. Caring about the dress could show a sense of style or lack of it which might indicate UI skills or other characteristics not related to programming, if you got a style own it and when people make the mistake in judgment you can correct them and move on with your life, thinking that people should not judge you by your dress is plain entitlement. As programmers we know the importance of patterns and ignoring thinking patterns of people and judgment patterns of people is disturbing.

Playing videogames can also point to certain characteristics, many male programmers who are into videogames will try to do do their own videogame, unsuccessfully but it will teach them a lot. They will sacrifice their social credibility in order to sit by themselves and code. I would assume they are more experienced in programming than a fashionista and I will be right in most cases.