Being a male geek/dork/nerd/outcast in school doesn't excuse behavior that causes a hostile, sexualized, or otherwise unwelcoming environment. I, a female geek, was an outcast too and participated in many of the activities you mention, yet I came out mature.
You claim that male engineers (which you referred to as neckbeards) just need to be told that their behavior isn't OK and that everything will work out fine. You know what, I've tried that approach many, many times and it always backfires. The first reaction is quite similar to what you have above. Blame the person for being oversensitive and blowing things out of proportion. Then other defensive reactions ranging from yelling to ostracizing the female from the group follow. Rarely, after lots of back and forth emails and other draining communications (where I have to do tons of research in order to educate them about male privilege and other concepts), the issue is resolved. This successful resolution has happened maybe three times in my career.
Guys, if you are faced with a complaint that something was sexist, not cool, etc., please, don't let your first reaction be the defensive reaction we see all the time. Take time, think it over, ask for more information so that you can understand her position. You might just find an opportunity to grow as a person.