Women were welcomed and encouraged by the government and society to work long hours in the war factories, as long as they gave up those jobs when the men returned. They were kept from combat duty, almost always employed in an auxiliary role, and rarely given promotions to higher ranks.
African-Americans served in segregated units, meant mostly to serve as supply units and graves details (with notable exceptions - see Tuskegee Airmen and armored divisions), and again, were rarely given command ranks. African-American civilians in war factories were paid less than whites until FDR signed an executive order ending the practice. In civilian life, they were still paid less tough, and segregated by Jim Crow laws.
Needless to say, women were still excluded from the battlefield in World War II and were restricted to rear line duties, primarily in a nursing capacity.
Avowed homosexuals soldiers were somewhat of a rarity. According to one published source, the military excluded known homosexuals because "it was considered a mental illness, and it was believed that they would hurt the productivity of the armed forces." Some psychiatrists did not enforce the screening process, and many homosexuals were allowed to join. Others simply lied about being homosexual and estimates are that thousands were eventually admitted into the various arms of the service to fight for their country.
Perhaps the most famous way that WWII showed racism (you can argue) is in the internment of the Japanese Americans on the West Coast. Where Germans and Italians were interned on an individual basis (if they were suspected of something), all Japanese Americans on the West Coast were interned.
You can also argue that racism showed up in the Zoot Suit Riots of Los Angeles where white sailors fought with Mexican American youths.
Finally, you can definitely see racism in the way that African Americans were not allowed in combat positions in the Navy and were not allowed in the Marine Corps at all.