Oh man, a guy who called me "Dude" would totally and completely annoy me. I mean, if he can't take the extra 1/8 of a second of brainpower to think enough to address me by some form of a feminine pronoun... I would interpret it as either laziness or just plain ignorance...
I think it's also because I'm a little older--"back in my day" we didn't call everyone "dude" and it's just one of those slang terms I never picked up on. My "homegirls" and I do not call each other homegirls, dudes, or any of that... if I use those terms it's just as the premise of a joke. I see the constant use of "dude" as a "young" thing... not that there's anything wrong with it (but yes, I do have a problem with calling girls "dude"--just seems disrespectful to me--and I figure God created feminine nouns and pronouns for a reason) but I wouldn't be dating anyone who called me, my friends, or parents by that term.
Calling a woman "dude" is, in my mind, the equivalent of calling a straight man gay.
Oh, just a hint of advice for all the "dudesters" out there--when interviewing for a JOB, do NOT go in and call your potential boss "dude". Sorry to slip in the old geezer advice...
The rare exception would be something such as what Shawny Boy pointed out--if it were an accepted term of endearment between a close friend or family member, I could handle that.