I feel like you're reading in a lot of things I didn't write.Some of the posts especially MMadsen's last one comes across like if you're playing a fantasy RPG if you're not white you HAVE to justify your existence in the game.
I will say, yes, if you want to play an African knight of Gondor or rider of Rohan, that takes some explaining.
If you're playing in a game world with kingdoms whose rulers live in castles, with walls covered in tapestries, and who ride out on war horses while clad in mail and carrying lances, etc., that is thematically medieval Europe, and I see nothing wrong with populating that land entirely with white people. I don't think it's racist or insensitive.
I also see nothing wrong with a made-up world with made-up races and cultures that don't closely resemble medieval Europe, etc. It gives up the resonance of Arthur's England or Tolkien's Middle Earth, but it works in its own way. You don't have to follow ERB's model of red men, black men, etc.; that's just a clear way of saying that the races involved don't correspond to real-world races and cultures.
Again though, if you go half-way and present a place like Arthur's England, but with a rainbow of different races from Imperial Britain's many colonies, that's jarring; it's "forced".