Is Tomb Raider somehow a bad game (Well, set of games!) because Lara Croft is female?
I wouldn't know because I would never buy a game that forces you to play as a female, such would be the predictable immersion-breaking experience.
If playing someone who is not very like you is an immersion breaking experience, I am curious to know what games you DO play.
How far do you take the idea that you can't play someone who is not yourself?