The Memphis Prince Chapter, What external conflict does Cassie refer to when she says, “I just don’t believe in fighting for nothing”?

Cassie is referring to race equality in the United States. In context, she is speaking with Mort, who is planning to join the army the next day. Cassie immediately responds that the war is dangerous.... that people are getting killed... that the whites in the United States, like Hitler, believe that whites are superior to blacks, and she mentions the "master race". Cassie doesn't want her friends and family to fight a war across the ocean to stand up for ideals that aren't respected in the country in which she lives. She wants to know if a war is going to change things for the African Americans.... the things that effect her.... the things that effect all blacks, namely, segregation.