In the UK yes, it's not done a lot but I've heard it. Among Brits, "mate" is just a term like the American "buddy," or "dude" -- and yes, I've heard some Americans say "dude" to a girl! It happened to me! And I didn't mind at all, it actually made me feel included. The guy who said it to me was a kind of alternative-culture musician guy who used "dude" a lot generally, and I said something in the conversation that he agreed with and he responded "Dude! I so totally agree because...." etc etc.
Then he stopped and said "Oh god I just called you dude, was that offensive?" I just laughed and said no way, I feel like one of you guys now!
In that context, things like "dude" aren't even necessarily gender specific anymore, and have almost become merely an exclamation now, like starting with "Man!" "Man, I so agree, that was the worst!"
Same with the British "mate." It's passed into a general term. I'm sure I've heard even a female call another female mate. "You're going be all right, mate." Totally normal. I think "mate" is even less male oriented than dude, in many ways.
If a guy calls a girl "mate" I take that as friendly and inclusive and like a platonic acknowledgment.
Even if a stranger I think it's fine. Passing in the street: bump into someone, a quick "Sorry!" Response a rapid "No worries mate." Even if a woman. I've seen, heard it and it's not a problem.