This is true in the long run, but not in the short run.
In the short run, not much changed in race relations and gender roles. It is, of course, true that African Americans moved out of the South to take jobs in war production. It is also true that women worked in jobs that had been reserved for men. However, this did not result in any real changes. It was understood that African Americans were still subordinate to whites and women were still subordinate to men. The women left their jobs after the war and segregation persisted.
In the long term, however, the experiences of World War II helped to change things. By the late 1950s and early 1960s, women were starting to push for different roles in society. By 1954, segregated schools were illegal. A few years after that, the Civil Rights Movement had started. While the war was not the only cause of these changes, it was important nonetheless.
The events on the homefront in WWII did not change race relations and gender roles immediately, but they did help to cause major changes in the long run.