Believability? You get shot and keep running? That's believable? How many weapons are you carrying? How many ammo types? How far can you run without collapsing from exhaustion? How can you drive/fly all those different vehicles? But a women just breaks it all, huh?
OK, maybe I shouldn't have added that specific word at the last moment without thinking more about it - but I felt like simply stating immersion was lacking something. Anyway, yes - sort of. None of those things break immersion like female characters do (in Battlefield! - there are plenty of places for female characters where they don't break immersion).
The number of weapons you can carry is quite limited in Battlefield, and it's not that unrealistic either (in that it's humanly possible to carry that much stuff). Ammo types? Not sure what exactly you mean, but seems like I haven't noticed it, so it's probably not that bad (although it's possible there are certain ammo types that are worse in this regard). Running is practically necessary for gameplay to be fun unless you want your game to be very realistic, in which case putting stricter limits on how much endurance you have can still have a harmful effect if not executed properly. Being able to drive and fly all kinds of stuff? Actually I do mind that stuff a bit, but at this point, that's pretty deep in what Battlefield is.
Female characters on the other hand? They're there just to fulfill people's role-playing wishes with no gameplay purpose at all while going against history. To me, it feels extremely out of place in a Battlefield game. There are probably tons of games where I have absolutely nothing against female characters, but Battlefield isn't one of them. Mind you, female characters can have a place even in a Battlefield game if it's written very carefully so it makes sense. Make the story or multiplayer battles revolve around settings where female characters were prevalent and it's all good. As far as I know, resistances had some female fighters, and I think there were female soldiers in the Red Army. Focus on them, make it all interesting, and it's all good. Slap female soldiers on battles fought practically exclusively by male soldiers, and it feels like it was done just meet the current trends.