I am a gen-x cis male who has been skateboarding and surfing since the early 1980's. The words "bro" and "dude" are completely genderless to me. I call my female friends and my wife "dude" all the time (bro less so as that might be a generational divide there). That said, if you, or anybody for that matter, told me that the term is harmful to them, I would makr every effort to avoid using it with them. I might slip up from time to time due to muscle memory, but if I did, I would apologize.

This is, at the very least, common courtesy. Your roommate is in the wrong and you are not being rude.