Context matters. I take it from your comment that you're a man. If you were in a female-dominated profession like nursing or elementary school teaching then yes, I think things like that would wear on you pretty quickly after a while. Every time, it would be a tiny little reminder that no matter how hard you try or how successful you are, you'll still be a bit of an outsider.[0]

Some people would probably be more consciously aware than others of the fact that the 3 letters "bro" are a reference to "bro culture". Here are a few groups of people whom I think would be most likely to notice: People new to tech; women who've had bad experience with "brogrammer" types; "brogrammer" types themselves. It seems like a bad idea to adopt any policy likely to make the first two of those groups uncomfortable while signaling approval toward the third.

[0] Side notes: 1. Those professions are making a real effort to change these patterns to be more inclusive, too. And 2. Gender inequality in tech is nevertheless a more pressing problem than gender inequality in nursing, because tech is considered a higher status career.