I run a GURPS Mythos campaign; Call of Cthulhu using GURPS rules.
GURPS uses points-buy for the entire character design, so you can pick and choose whatever stats, skill levels and other features you want up to your maximum points level. It also uses Disadvantages where you get points back for disadvantaging your character in some way. One of the options is to be badly viewed socially in some way. In the 1920s game I run, for example, you might choose to play a black character, a known homosexual, a Communist, or whatever, and get points back because the majority of people you encounter will treat you badly (whether hostile, patronising or dismissive doesn't matter for mechanical purposes).*
This is a system that also works using minority races or cultures in fantasy, and I am setting up a Fantasy campaign using GURPS where one player is choosing to play a goblin. I have warned him that people will treat him like crap, and he is happy to play against that.
* I ought to point out that this is optional for the player. If you choose to design a character from an historically persecuted section of society but don't want them experiencing 1920s attitudes then you don't need to take the disadvantage.
