I've lived in California for 27 of my 41 years, about equally split between SoCal and Northern California, and I have never heard someone call a woman 'dude' without it being a mistake or a joke.
The Atlantic notes that women use "dude" to address other women[1]. I'm not from California, and I'd agree that the most typical usage seems to be towards men, but I have heard women refer to other women as "dude".
There are two distinct uses of "dude". One is as an exclamation (not a form of address). "Dude, I'd never do that" is the approximate example in the article, and a woman might say that to another woman. She is not calling the other woman a dude. Test this claim by trying the following: "Man, I'd never do that." "Gentleman, I'd never do that." "Fellow, I'd never do that." etc. The use of "man" and "dude" as an exclamation has made it into everyday conversation. "Man that sucks!" has become an expression of dismay devoid of gender and indeed not even directed at any particular human.
Then there is the use of "dude" to refer to a specific person (singular). This is a very rare use of "dude" in reference a woman, and usually is used as commentary rather than a literal descriptor, or ironically. "She's such a dude." It is definitely making a comment on gender or stereotypes.
I would be very confused if you referred to me as a dude in everyday conversation, wondering what you were trying to say. On the other hand, I did recently say about myself, "I'm such a dude" when making a comment about my approach to an unfortunately often-gender-stereotyped activity, housekeeping.
