Barbara Smith Conrad, a black child of the segregated South, did not seek to vote or to ride in the front of the bus. She just wanted to sing.

But in 1957, when this mezzo-soprano from a small East Texas town was cast opposite a white male student in a University of Texas, Austin, opera production, that was just as controversial. Suddenly Ms. Conrad was thrust into the drama of the larger struggle for civil rights. Her story is now the subject of “When I Rise,” a documentary scheduled to have its national television premiere on PBS’s “Independent Lens” on Tuesday night. (Check local listings.)

Objecting to Ms. Conrad’s casting, segregationists in the Texas Legislature threatened to withhold state financing from the university. University officials yanked Ms. Conrad from the production — Henry Purcell’s “Dido and Aeneas” — replacing her with a white student. After the incident made headlines, Harry Belafonte stepped in, promising to pay for Ms. Conrad’s music education anywhere in the world if she chose to leave Texas. Instead, she stayed....