Urban Dictionary entry for bro:
"An alpha male idiot."
You can whine and moan about fine semantics all you want. Doesn't change the fact that Bernie Bros are shallow, unintelligent, loud-mouth people. That which we call a bro, by any other name would smell as rank.
By fine semantics do you mean supporting the term pulling examples from people who aren't even male? Because some of the first articles to use the phrase picked up examples from women, all the while clearly labelling it a male phenomenon.
Anyone who tries to pass the "bro" thing off as not really being about gender doesn't see it for what it is (or doesn't want to admit it), which is Hillary's campaign pushing charges of sexism again. That Bernie inspires sexism. If it's stated as a matter of Bernie supporting men attacking Hillary it's easy to frame as sexism.
There are obnoxious people like you describe who support Bernie Sanders. As there are for Hillary, and Trump, or whichever candidate you support. This turned into the narrative it has specifically to single out and attack Bernie, not because it's some kind of unique problem that has to be dealt with somehow.
It's also kind of amazing seeing it picked up by people on the right.. you do know that this is a tactic done on Hillary's behalf, right?