I'm a 29 year old male and I don't understand the argument that you cannot empathize with another gender or person with a different background.
I've played Metroid games and I adore the recent Tomb Raider games, and I've never once had a problem with the character being a girl. In fact, looking back on early PlayStation days in the 90s, those early a TR games, my friends all thought Lara Croft was really cool and they loved those games.
Personally, I just don't see the problem. Would I choose a girl if it's a game where you choose your gender and looks, etc? No, probably not. But would a girl choose to be a dude in her playthrough of the same game? Probably not.
But for games where the protagonist is a girl and it is what the story is, I just don't see why someone of the opposite gender would have a problem with it. Just enjoy the game.