And I'm not trying to downplay any bad behavior by people you've had to interact/work with. Pretty much anything can be used in a negative way in a specific context, and people can be huge jerks. I'm merely trying to say that words which you think are offensive to one gender, can be used as a completely neutral term without any subtext other than friendliness. It's really a shame that this word has become so negative to you.
I also call my (female) SO "bro" – in addition to a broad range of friends and family – in specific contexts. But I would never consider the word neutral or inclusive in the context of the tech community. Too much baggage. If any of the people I call "bro" were programmers plugged into the same world we are currently plugged into, I would not do it, period.
The fact that everyone in this thread came into this with knowledge of the term "brogrammer" suggests to me that there shouldn't be much of an argument, but I guess that's just wishful thinking.
I'll continue to use the word "bro" because in my timezone (and on a few on either side) it's not a term of offence.