First, I am a white male individual, just to be clear.
Secondly I don't care, and nobody should. If the writer of a game has chosen to tell the story of character x, which happens to be race y and sex z, then fine. Who am I to tell him what to do?
When given a choice, lots of times I go with the default character. In Mass Effect, for example, I found the default Shepard good enough looking and the voice matched great with his face. I've seen some odd user creations in this game, which subtracted from the feel of the game by trying to use the editor and failing (I've yet to see a great custom Shepard).
Other times I try to create weird characters, like in Destiny beta, I chose to create an Exo Warlock. Or I sometimes create female characters, or whatever other options are there (in ESO i created a female redguard, for example). I like the games that give you choice, but it should be justified by the genre or story or something. THIS SHOULD NOT BE IN EVERY GAME. I don't want to play Uncharted as a woman, or Tomb Raider as a man, or Beyond Two Souls as Willem Dafoe.
I hated the controversy around The Puppeteer (great game, btw), when people were complaining for not having the option to play a female puppet. Well, dooh, it's a story about a BOY who lost his head. BOY.
I belive that people who have problems with the lack of choice in some games are the real racists/sexists/homophobes/etc., not the creators of the games. Because they are the ones that actually CARE what race/sex the character is and act with rage against the game (Far Cry 4 controversy, anyone). All the other people who don't care and aren't hateful against anybody, just enjoy the game regardless. Why is race, sex or sexual orientation an issue in 2014 baffles me. We are all people with equal rights and status. This is not and should not be an issue.