I would avoid it if it was a slur that belittles other people. So no. If you choose to be offended by a word that young men in North America men use to fraternize, it's your problem. I'm not even American and I really couldn't care less when my American coworkers call me "bro".
Let's say I find dogs offensive and dog owners alienating. Is it reasonable for me to ask the society to be more mindful of my feelings and make people stop walking dogs while I'm out? No, and I think we can agree that a person making such a request would likely be borderline mentally ill, or at the very least, unadjusted to living in the society. So where do we draw a line between mental illness and a simply asking not to be excluded? If everyone's opinion is equally respected, who is the authority that decides what's reasonable and what's not? Let me guess, you? Because it furthers your purpose right?
In fact, I've just remembered we have a git branch at work called "bro". Makes me realize the dire implications of a simple joke like that - we could potentially get sued by an intolerant employee. No wonder companies have started looking for culture fits these days, it's become very risky and expensive to hire people who are different because there is a good chance they will sue over frivolous reasons. Not saying I am like that, but can you see where I am going with this and how this mindset is actually damaging to minorities? Can you see how many employers would just choose to not hire a minority person simply because they are afraid of the implications? This way of thinking does MORE DAMAGE than good. Does what I wrote make sense?