On the day he was sworn in as governor of Georgia, Jimmy Carter, an ambitious white peanut farmer from rural Sumter County, announced that “the time for racial discrimination is over.” The declaration landed like the carefully calculated bomb it was intended to be in the South of 1971 — and landed Mr. Carter on the cover of Time magazine, along with the blurb, “Dixie whistles a different tune.” But in his ensuing half-century of public life, Mr. Carter, the one-term Democratic president who died Sunday at 100, would be forced to listen rather helplessly as Republicans mostly called the...