Have LBJ choose his Great Society over the Vietnam War and have Martin Luther King, Jr., avoid being killed in Memphis. LBJ also must give his speech in New Orleans on race and the need for the South to look beyond racialist politics. Maybe have King there alongside him in front of that majority white crowd.
The Reagan Revolution was in many ways caused by the collapse of the postwar economic order, which assumed scarcity not to exist (and which was proven so very wrong in the 70s), but also by a growing distrust with the state on matters of the role of the judiciary, the perceived coddling of criminals in a country with shockingly violent and growing crime problems in the 70s, and more nebulously, a desire for optimism, positivity, and a break with the painful recent past.
The crisis of the Welfare state and of the idea of industrial policy are two issues that, had LBJ devoted a lot more resources to, might have merely exacerbated the inevitable crash back to earth after the OPEC crisis. The government was already crowding out investment with its existing tax rates, but add more entitlement programs and a universal basic income (which King proposed) to it, and the American economy is likely going to get even harder hit by the German and Japanese competitive wave in the making.
As for King, keep in mind that King, much like JFK, is remembered so fondly partially because he was assassinated. King's popularity in 1964-1965 were at very high levels nationally, among people of all races. After 1966, after the radicalization of SNCC and the growth of the Panthers and the idea of Black Power, his popularity among African American activists in particular dropped. After he came out against the Vietnam War, many liberals who had previously supported him began to rethink things and his popularity dropped further. Fundamentally he was losing popularity and losing it quickly.
Defining how the Vietnam War is "not chosen" might be important here as well. South Vietnam after all was not in real danger of being overrun until the NVA got into the fight. However, once they did, without American air power and ground support, they probably do not last all that long.