Not to everyone, and that's cool, until someone tells you not to call them dude anymore. Then your an asshole if you try to argue the gender neutrality of the term dude. Such as telling someone to get over it.
You're arguing that the context is subjective to the word provided yes? Yet your example is also subjective, clearly when your friends call you bitch it's not meant as an insult. I can't think of a single instance in which using dude as an insult is going to get someone offended on purpose, where bitch definitely can be used purposefully.
Dude can be used as an insult when used to refer to someone who specifically said they don't want to be called dude. I don't know why this is so hard for you. If people don't want to be called something, don't call them that. Definitely don't tell them it's their fault if they're offended and they need to get over it.
Yeah that's not how language works, that's how pestering works, just because you don't like to be called Apple and I call you an apple doesn't mean that apple is now magically an insult word.
Is it really that hard to not call someone dude if they asked you not to call them dude? Just accept they don't like it and continuing at that point is rude at best.
Have lots of friends that calm me bitch. They can do so because I'm fine with it. If I tell them I'm not and they reply with "get over it", we have a problem.