Liberalism, the belief in freedom and equality, is the American mainstream, and the same is true throughout most of the West.  The liberals in the sixties were as anti-communist as the conservatives.  The Left, then, were the communists, and the Right were the people who opposed labor unions and integration.  Then, the Right found political advantage in calling people who supported labor unions and the mixing of the races Leftists, a word they also applied to hippies (and, earlier Beatniks  the "nik" suffix came from Sputnik).