A wedge issue is a political or social problem with a controversial nature. It divides a demographic or population group. They´re often used to weaken the unity of a population. In cases of a racial wedge, it refers to the intent to separate population groups attending to their ethnic group.
For example:
George W. Bush’s presidential campaign was in danger in February of 2000. John McCain had just scored an unexpected victory in New Hampshire, and his candidacy tended to triumph in numbers.
The Bush campaign was fighting to survive, so members of the political section start using a racial wedge for political gain.
South Carolina voters started suggesting that McCain’s adopted daughter from Bangladesh was really a Negro child he fathered out of his marriage. By the end, Bush scored a primary victory.