The "women are always screaming" stereotype is sexist. It's a direct extension of the pseudoscientific hysteria diagnosis that used to be commonly accepted. "A women," as you put it, might scream, and you might find that annoying. Women as a category have higher pitched voices on average, and the line between "reasonable yelling" and "hysterical screaming" is often just one of pitch, even when the cause for alarm or injury is the same.
Additionally, neither I nor any of the women in my life "scream" in response to injury. We yell in pain just like someone with a masculine voice, if a bit higher pitched. Some may, but it's not common and is usually reserved for situations of extreme alarm or fear, or occasionally excitement. Any time a woman does scream on video, you always see someone in the comments complaining about how annoying women screaming is. The same is never said about men screaming, unless they scream "like a girl."
9/10 times. How out of touch are you?
Eivor was a foreigner (and an invader) for everything outside the beginning of the game, so was Kassandra/Alexios (also invaders), they just had the same skin tone as the place they're foreign in. There's a big difference between "native characters with understated culture" and just "not foreign." Those are totally different arguments, and it seems like you're trying to make both. Again, why not have an interesting character from history be explored like this. Acting as if past characters are these nebulous "local" individuals when they're often the direct children or relatives of prominent, real, historical figures, if fictional ones, seems silly. This is totally in line with past stories they've told. I really don't see a valid reason a non-local character is "problematic" in an AC game. We've done it a bunch of times. We've played a Welsh guy in the Caribbean, a Viking in Britain, and a Spartan in Greece, just to name a few. I'm sure I'm forgetting other valid examples.