Late 1960s-early 1970s. The traditional left consisted of social democrats who were too connected with the establishment, and socially conservative soviet-style communists. The new left rejected racism, war, and imperialism and wanted all power for the people.
I don't know what you mean by new right. There were Neo-Conservatives who rejected traditional conservative values of lesser government because they wanted a robust national defense. They were also tolerant of needed social programs. Then you had your old Ku Kluxers and Nazis whose influence was declining.
A paradox is Nixon. He was a rabid anti-communist conservative, but he nationalized passenger rail service, did wage and price controls, fuel rationing, recognized China and made peace in Vietnam. Then he got the boot for spying on the Democrats.