I've worked at Amazon and Google, and I don't know where this idea of the "tech bro" or "brogrammer" being omnipresent in tech companies came from. I know maybe one person who might fit this description. It just seems like an insulting label that someone came up with because they hate tech companies and gentrification, and then the media decided to run with it because it made for entertaining news. Is there any actual data showing that "tech bros" constitute a substantial % of the tech industry?
The way I see "brogrammer" used these days is basically like "hipster": it means 'people in [incredibly broad category] that I don't like'. For the hipsters, the category was young adults in urban areas, and for brogrammers, it's young adults at tech companies. It's just a way for people to pretend that their personal prejudices are actually the fault of the people they're prejudiced against (similar to the old "welfare queen" stereotype).