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.