Does homophobia exist within the Star Wars universe?
No, but because homosexuality used to not exist in Star Wars as a matter of policy according to some sources.
While George Lucas was in charge of Star Wars, some admins and creative directors essentially said that homosexuality did not exist in the Star Wars universe. George Lucas himself remained largely agnostic about the idea, never openly supporting or opposing the idea, while a few homosexual characters popped up in books every once in a while. Homosexuality in Star Wars always had a very negligible presence, if any at all.
In 2009 however, the game SWTOR (Star Wars Knights of the Old Republic) had the opinion that homosexuality did not exist in Star Wars. They took this so far that the game admins were shutting down conversations about homosexuality on the message boards. To quote on admin:
"[on homosexuality] As I have stated before, these are terms that do not exist in Star Wars.
Eventually they apologized after it erupted into a scandal.
This issue came up because traditionally many Bioware games, like Mass Effect, allowed you to pursue a homosexual relationship in game. Suddenly in SWTOR you couldn't romance the same sex, but still could romance the opposite sex in conversation options.