Personally, I call even my mother "bro", but if anyone expressed that they didn't like being called it, I would make a concerted effort not to call them that. It's not hard to try in good faith.

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.

No, you're allowed to be reffered to how you want

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

Am I in the wrong here?

No. It is okay to have boundaries around pretty much anything, even if it goes against what someone or somemany else usually does.

"But I call everyone 'bro' or 'dude'!"

Sure, I get that! But not me though.

It's likely a bullshit excuse for deliberate disrespect. Return the favor by finding something to call them which bothers them - when they complain, give them the same excuse they use in return.

1. Yar aint wrong.
2. correct /c/
3. Straight up start call’m “baby,” “doll,” “girl,” “bitch,” “cunt,” “yapper,” etc. until they start getting offended. “Maybe you can now empathize why I don't liked to be ‘bro”d’? Truce?” Some folks only learn the hard way.
4. Indefensible argument:

citing ideolect as a defence.
“You talk to your grandparents this way cunt?” e.g.

No, your friend is in the wrong. I use dude and bro a lot, and for everyone. I use it irregardless of gender. HOWEVER, I also respect others. If someone is uncomfortable with how I am referring to them, I accommodate. Because it costs me nearly nothing to change the way I talk, and I likely would be having a harmful impact on whoever I am talking with if I don't respect their boundaries. This is particularly the case for trans folk, cause refusing to accommodate only worsens the impact of gender dysphoria.

The only time I have ever given pushback is when someone tells me not to use the word "queer." I am queer, and I identify as gender-queer, and I will not censor my identity.