Drive Club had the Gender option, plus a few different Racial characteristics if I remember rightly. Also, didn't one of the Ridge Racer games have a Dual between 2 Female Racing Drivers as the main storyline ?
But it could all get out of hand pretty quickly.
Choose Gender - Options - Male / Female
(ok so far ?) what about those who don't like to label themselves as either of those 2 ?
Choose Race - Options - .........OMG I started doing a list & deleted it, as several options could be seen as Stereotypes.
Build Type (Male) - Options - Youth / Thin / Slim / Athletic / Body-Builder / Slightly Overweight / Obese / STIG's American Cousin*
* Please note that when selecting this option, your Avatar will only be able to fit into the Truck !!