I don't really care, personally. Male or female, black or white, human or otherwise... A main character is but a device through which a story is told, and each type of character has their own unique ways to contribute to a story. As long as said character is interesting, I'm game. Heck, if anything, I enjoy when we get an unusual main character, because they can (potentially) offer some interesting details in a game that others normally wouldn't.
I don't really view their gender/nationality/etc. as a potential impediment to my immersion in a game, because even if the majority of the game is shown through their eyes, I don't really consider it a truly "first-person" experience. I feel like I, as the player, am just a sort of bystander or observer of the events around this character, despite any direct control I may have over them in the game -- I'm just tagging along for the ride, and offering suggestions on how to go about things throughout their story. Perhaps I'm just overly aware of the divide between the fantasy and reality (despite being a bit of an escapist)? I mean, after all, a game is a game. No matter how direct of control you may have over the actions and consequences of a game, it's all taking place within a fantasy realm, so you're not actually "doing" anything, per se. The character you're playing as is the one doing everything, and their actions and words are the medium through which their story is conveyed to you.
Granted, with all of this talk of stories, you may be able to tell I'm an RPG fan. (Plus various adventure games and whatnot with strong plots.) If we're just going to talk about a game you hop into and shoot stuff, or play a sport, or whatever, thennnnn... Well, I guess this ties into the other side I was going to bring up: custom characters. In games that allow you to create your own character, I usually play multiple characters -- at the least, one guy and one girl. Even if there are no statistical differences between character types, I just like to have some diversity available to me. (I also simply enjoy the creation process, so changing things up presents some creative challenges.) It keeps the role-playing fresh. On the other hand, if a game forces you to pick, for example, a guy for one role or a girl for another, then again, this doesn't matter to me. I'll look at the advantages and disadvantages of each character type, and then usually play each anyway, for the sake of the change of pace. (Being a guy, of course, I'll usually start with a guy, especially since I have a sort of OC I base most of my characters on. But I usually switch off to a girl at some point, and then alternate as desired.) If only the male human character is able to use big weapons, then I'll play as him for the weapons; not because he's a dude. Likewise, if only the female alien character can use stealth, then I'll play as her for that purpose, and it doesn't bother me that I have to play as a girl (nor an alien, or whatever other race) in order to use said stealth abilities. If anything, that kind of exclusivity just gives incentive to play other types of characters, and I enjoy them all for their own strengths and weaknesses.
