In the original trilogy we only see four different light sabers with three different colors: blue (Luke's, originally Vader's), blue (Obi-Wan's), green (Luke's), and red (Vader's). All three characters used blue at some point, the unique colors are just unique colors, the movies say nothing about it.
For fans of the movies, red became associated with the dark side because of Vader, and blue/green became associated with the light side because of Luke and Obi-Wan, but nowhere in the movies is there any indication that the colors are anything other than cosmetic. All the lore about light saber crystals was made up later.
In any case, lore doesn't really matter much here, especially since lore has little to say about light saber color (aside from the EU, which doesn't really count for much).
What matters is that there have to be some restrictions in this game. Should anything be restricted to light/dark side in the game? Why? There's no lore saying so. But in this type of game some restrictions have to be put in place.
Luke used blasters in the movies, so why can't my Jedi Guardian use a blaster? Because this is a game. Han used a light saber once, so why can't my gunslinger equip one? Because this is a game.