I think this “diversity” has been part and parcel of urban fantasy since its inception, not a “modern” phenomenon.
Unfortunately, no contemporary style urban fantasy tabletop game I know of has tapped into this zeitgeist and been able to get noticeable market share. Shadowrun is post-apocalypse cyberpunk, so not contemporary. The White Wolf games were not designed for mixed play and so suffer from extensive power creep (not to mention a bazillion different editions and associated edition wars, which has soured me on the whole fandom). Nightlife, Everlasting, WitchCraft, Nephilim, Nightbane, etc (basically any game that tried to have mixed play and universal rules at the onset) all died out in obscurity.