The great depression in a way helped unify the African american minority in the U.S. When the National Recovery Act (NRA) was passed in 1933 it was meant to help all people get work without discrimination but it didn't turn out that way overall a lot more whites were hired and received higher wages then African Americans. In 1929 the St. Louis Urban League launched a national “jobs for Negroes” movement by boycotting chain stores that had mostly black customers but hired only white employees. This situation also lead to the founding of the National Negro Congress in 1936 and the Southern Negro Youth Congress in 1937.
As for during WWII the military was still segregated but during battles it is hard to keep segregation. Many African Americans did still question why. James Thompson, an African American serviceman, wrote to the black newspaper, the Pittsburgh Courier, and asked "Should I sacrifice to live 'half American?' This started what is known as the double V movement. the double V movement stood for victory of democracy abroad and at home. After the war they returned to a still segregated world but they were more motivated then ever in trying to get equality. It is also good to note that many white servicemen returned with new found respect for there African-American brothers in arms and were more supportive of the civil rights movement.
Sources:
http://socialistworker.org/2012/06/28/blacks-and-the-great-depression
http://www.livinghistoryfarm.org/farminginthe40s/life_18.html