Definitely Shadowrun, especially when you take into account Earthdawn, which has a similar level of worldbuilding that ties into Shadowrun. From a character creation perspective, the "ground-up" style of Shadowrun allows whatever type of character you can dream up. The Shadowrun novels had all manner of inclusivity, and actively explored some LGBT themes in the early 1990s.
In a more modern setting, the Dresden Files books and roleplaying game I think do a great job of having a really rich and inclusive world.