In the films (and canon cartoons) a number of species seem to have races based on differences in skin colours.
Twi'leks definitely appear to have different races with big varieties in skin colours and lekku shapes.
Oola - Return of the Jedi
Aayla Secura - Attack of the Clones & Revenge of the Sith
Orn Free Taa - The Phantom Menace, Attack of the Clones & Revenge of the Sith
Bib Fortuna - Return of the Jedi
Togruta also appear to have races based on differences in skin colour, all on the red side of the spectrum (reds, oranges, yellows).
Ahsoka Tano - Rebels
Shaak Ti - Attack of the Clones & Revenge of the Sith
Humans are displayed as a variety of races, Black, Caucasian, Asian.
Lando Calrissian - The Empire Strikes Back & The Return of the Jedi
Mace Windu - The Phantom Menace, Attack of the Clones & Revenge of the Sith
Obi-Wan Kenobi - All the films in one form or another
Han Solo - A New Hope, The Empire Strikes Back, Return of the Jedi & The Force Awakens
Kanjiklub - The Force Awakens
Nothing ever seems to be mentioned regarding races. One would assume with a wide variety of species throughout the galaxy racism within species would have given way to speciesism against those with far greater differences than mere skin colour.