Absolutely not wrong! We all deserve a minimum level of our preferences in address being respected.

Now, is it true that dude in specific, and bro to a small extent, aren't about gender per se? Sure. Dude was originally gender neutral in the surfer lingo. And brospeak litters conversation with bro like cigarette butts on a highway. It isn't being used as a slight or a misgendering the way you describe it.

Like, I tend to litter both speech and casual writing with "like" at the beginning of sentences like this. Bro is used akin to bub or pal or homie more than the origin as brother. It isn't as gendered as it started out. Dudettes even use bro for their sisters ;)

That doesn't change that someone you live with is brushing against your specific pain points.

This is a situation that requires compromise on the part of a roomie. When an aussie rooms with someone that suffered abuse by being called cunt, it only matters a tiny bit that they don't mean it in a bad way. It matters in that it's something to work on rather than an immediate deal breaker. Your situation is a few steps apart that, but the same principle.

You're absolutely not being rude. And, if the person in question refuses outright to work with you they're the asshole. Language, ideolect, takes time and effort to adjust, but it is malleable. That effort is necessary when addressing someone. They can still call others bro. They can still use the term bro as a term of affection. They just need to stop calling you bro. And dude, despite its origins.

Fwiw, while I definitely believe this is an appropriate community for the question, it would also be appropriate in any general questions community. It applies outside of trans issues as well