Well aktually, Johnny Cash issued a statement to the KKK telling them his first wife wasn’t black and appeared to have some racist attitudes in his youth, though he did come around later on and I wouldn’t say he was racist. Her heritage is described:
“In the image, Vivian, whose father was of Sicilian heritage and whose mother was said to be of German and Irish descent, appeared to be Black.”
Though in other images in the same article she doesn’t appear black at all, so I’m not sure. There seemed to be different attitudes about what was considered “black” in that time.
“The stress was almost unbearable. I wanted to die,” she [Vivian] wrote in her memoir. “And it didn’t help that Johnny issued a statement to the KKK informing them I wasn’t Black.” She did not think the campaign should have been dignified with a response.
So she may have been more upset that he responded at all, not necessarily being upset that he said she wasn’t black.