Here in Yankee Stadium’s locker room after Game 5 of the 1952 World Series, Senator Richard Nixon of California, Republican nominee for vice president, congratulates Jackie Robinson on the Brooklyn Dodgers’ 6-5 win over the Yankees. (The Dodgers ultimately lost in seven games.)

In 1960, Robinson endorsed Nixon for president, declaring that the civil rights commitment of Nixon’s Democratic rival, John F. Kennedy, was “insincere.” In those times, an African-American Republican was by no means unusual. About 39 percent of black voters had supported the re-election of President Dwight Eisenhower and his vice president.

Then, in October 1960, Martin Luther King Jr. was jailed in Georgia on a trumped-up charge. Kennedy made a much-heralded telephone call to King’s wife, Coretta, which helped to get King released. Declining Robinson’s insistence that he intervene in the case, Nixon told him that Kennedy had opportunistically made “what our good friend Joe Louis called a ‘grandstand play.'”

Jackie withstood intense pressure — including from his wife, Rachel — to follow King’s father in switching from Nixon to Kennedy; he later wrote that his decision had “something to do with stubbornness.” As a result, a ballplayer who had withstood death threats in 1947 to break the major leagues’ color barrier was denounced as a “sellout” and “Uncle Tom.” That November, Nixon won only a third of the African-American vote, a crucial factor in his hairbreadth defeat...