CHARLESTON, SOUTH CAROLINA—Maryland governor Wes Moore, who is widely expected to seek the 2028 Democratic presidential nomination, has a powerful family story of racial injustice that he repeatedly tells during public speeches: His grandfather, as a small boy, fled 1920s Charleston with his family in the dead of night after his father—a prominent black minister and Moore’s great-grandfather—angered the Ku Klux Klan with sermons condemning racism. Narrowly escaping a lynching, the family took refuge in Jamaica. But Moore’s grandfather, just six years old at the time, vowed to return to America, where he eventually raised a grandson who made history...