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.