I'm not sure I would want to put restrictions on profession based on race or sex. Sure, historically there were not many black female marshals, and perhaps I'd put some restrictions on what job a PC could have, but if a PC wants to be the only one and can come up with a decent rationale for it, why not be flexible?
After all, history was a lot more complicated than those black & white westerns portrayed it to be. Indian tribes may have adopted white kids or black kids, or Indians may have been adopted by white (or black) families. Slaves escaped throughout the Antebellum and U.S. Civil War periods and some of them managed to at least pick up skills that ordinarily were reserved to white males.
Of course, part of the equation is whether the GM wants a historically accurate game, or more of a fantasy game. If the game is going to have fantasy elements, then I don't see a reason why it also can not have characters who managed to buck the prevailing stereotypes.
For example, suppose a PC wants to be a black female sherrif. Of course, there would be no way in tarnation that she could get deputized. So she went west, learned to shoot, found some gold, and the gold-miners who formed the nucleus of the boom town were okay with having her as their sherrif, especially since she could shoot an ant crawling up your pants leg from 50 feet away, and not hurt your leg, unless she wanted to.
(Think "No Name City" from Paint Your Wagon? I don't think they would care who was sherrif as long as it was someone who did a good job at keeping thugs and claim-jumpers out without cramping the drinking and gambling. When the farmers come in later, they may be amazed or even horrified, but what are they going to do about it? Maybe eventually somebody comes by and does something about it, which is why the PC left that town and joined this adventuring party.)
I might actually use a character like this someday, especially if I ever run a Deadlands campaign. My point is that just because there is no character like that in the history documents, that does not mean that a PC can not be a character like this. Just don't expect the kind of official position that a character on a purely fantasy would could have.