It's no surprise that a novel written in and about the American South would have something to say about race. It's just about everywhere in The Heart is a Lonely Hunter, but while the novel has both black and white characters interacting, it is about much more than race relations. McCullers is too busy focusing on her characters' humanity. Indeed, African American author Richard Wright praised Carson for her "astonishing humanity that enables a white writer, for the first time in Southern Fiction, to handle Negro characters with as much ease and justice as those of her own race." (Source.) In doing so, McCullers sheds light on the fact that many of the novel's white characters are completely unconcerned with or even oblivious to the issues of race, which makes them unthinkingly reinforce the unfortunate status quo that dominated the South before the Civil Rights Movement.
McCullers' black characters don't do much to challenge the racist status quo in the novel. She depicts them as complicit in the town's racist attitudes.
This is not a novel about race. Rather The Heart Is a Lonely Hunter uses the issue of race to tackled the larger issue of identity.