Nah, mate is as gendered as dude. Like sure some woman won’t mind, but it’s mostly men being called mate by other men.

Well, yes and no, depending on where you’re from.

Where I’m from, I’d say mate meaning “a person who is my friend” as opposed to mate meaning “greeting to a random person” are used a bit differently. I think it’s normal for anyone of any gender to refer to someone else of any gender as one of their mates. I would say it’s not uncommon (though less common, for sure) for women to greet other women. But men and women generally refer to someone of the opposite gender as love (and of course this is looked down upon in other parts of the country (other terms of endearment are available, but love is the most common, at least when I lived there)).

I’d agree that no straight man would be likely say “I had sex with my mate”, but I don’t think they’d be much more likely to say “I had sex with my friend”, either, unless they ended the sentence “… with benefits”.