What illness sounds respectful to white folks in A Raisin in the Sun?
It is the "flu" which sounds respectable to white people.
In Act I, Scene 1, Ruth wants to call in sick. Mama says she'll call Ruth's boss, commenting, "I'll just call her up and say you got the flu". When Ruth laughingly asks, "Why the flu?", Mama responds, "'Cause it sounds respectable to 'em. Something white people get, too. They know 'bout the flu. Otherwise they think you been cut up or something when you tell 'em you sick".
Mama is referring to the atmosphere of racism and racial stereotyping that is the primary theme of the play. Even though the days of legalized segregation are supposedly over, the attitudes that spawned such blatant discrimination still prevail. White people think of black people as different from themselves - violent, lawless, and uncivilized - so that when a black person calls in sick the immediate perception is that they have gotten "cut up" in a brawl or gang fight or something. The sense is that the things black people suffer from are somehow the result of a propensity towards more shady living. To have the "flu" is more "respectable", because it is something white people, who of course are better than that, fall victim to as well.