Create a timeline where racial segregation in the US still exists with a POD no later than the end of World War II.
By later, do you mean "no POD's before WWII?"
Anyway . . . to continue . . . Nixon wins (ie Daley and LBJ don't cheat so much) in '60, and he starts pursuing the infamous "Southern Strategy." Nixon wins in '64, but his presidency sees the heavy deployment of combat troops in Vietnam, rising student opposition to the war, and the federal government looking the other way while southern states ruthlessly crush civil rights demonstrations. After MLK's assassination at a Civil Rights march (1963) the civil rights movement sees a much earlier turn toward more radical means. This is combined with increasing student militantism in the face of heavy-handed police actions against the anti-war movement (mainly student-manned and organized as OTL), combines to create a tension filled '68.
JFK is running for the presidency again, and is widely seen as the last best hope for civil rights and student anti-war movements that are turning increasingly violent. On the other side, Ronald Reagan, in a metoric rise through Republican ranks, appears to be the candidate of the GOP after just 2 years as Governor of California. JFK's assassination during the primary campaign ends hopes of a united Democratic Party, and in Chicago a brutal floor fight results as a grieving RFK leads JFK's youthful supporters in an attempt to keep the nomination out of the hands of Hubert Humphrey. RFK's attempt fails, and he refuses the vice-presidential nomination, and refuses to campaign for the Democratic candidate, fatally wounding Humphrey's bid for the White House.
Ronald Reagan is elected in 1968, and the next 4 years sees rising violence, as radical anti-war and civil rights activists take up violence to oppose the Reagan Administration. The violence reaches a peak during the 1972 presidential campaign, when President Reagan is wounded in a failed assassination attempt. The attempt is used as an excuse to take massive action against the radical leaders of the anti-war and civil rights movement, and the so-called "Los Angeles Eight" trail runs parallel to an epic presidential contest between RFK and Ronald Reagan.
This doesn't really take us to the present day, but I don't really want to think about another 4 years of Reagan after '72, cause if you though Nixon's White House was criminal, imagine it after 12 years of power, [shudder] . . .