I think what you'd need to do is make the 'Southern' mindset more acceptable up North. If the Dixiecrats pushed for segregation elsewhere, the people who got pushed would just dig in their heels (FBI agents driving through Michigan towns seeking out 'race mixers' in a sullen, uncooperative populace while diners de-segregate as soon as they are out of sight and Klan members get whipped out of town or disappear at night.)
I think the 1880s and 1890s would be a good time. 'Scientific' racism became fashionable, and if any party thought it a vote-winner at the federal level it might well have gone into the mainstream nationwide even more than it did. It could being the South on board - remember 'Birth of a Nation' - and allay northern fears about 'hyphenated Americans' and the great unwashed debarking daily.
Another point (overdone, but possible) would of course be the 1930s. You don't have to have President Linbergh, though I think he has sort of become code. Say the Klan isn't rocked by scandals but instead continues to build up its (alarmingly large) northern followership, crime and racism are politically linked, and when the epression hits, divisive politics play out with greater success ("Jobs for Americans! Get the niggers and wogs out of our factories!"). Instead of Roosevelt's 'Socialism Lite', you'd get Compassionate Fascism.