In general, the Soviet leadership was ambivalent about the New Left and this mirrored the generalized ambivalence the New Left held for the USSR. Although the New Left espoused a harsh critique of American society, their ideological focus was more in line with younger communist movements and leaders like Mao, Ho Chi Minh, or Che. Brezhnev and other Soviet leaders had experience with this type of ideological independence with both Tito and Mao during the 1940s and 50s and that had led them to be leery of ideological movements that deviated from Marxist-Leninist orthodoxy. The fact that the SDS did grew out of an American progressive milieu instead of the American Communist Party added a further layer of skepticism for Soviet leaders.

Moreover, the New Left would also occasionally critique Soviet actions; one of the precursors of the New Left in Britain, the Communist Party Historians Group, which included such luminaries like E. P. Thompson and Eric Hobsbawm, openly critiqued the Soviet invasion of Hungary in 1956. There were similiar sentiments over the Soviet's crushing of Prague Spring. Graffiti both at Berkeley's and Chicago's1968 protests drew explicit connections between American police actions and Czechoslovakia. While this graffiti (welcome to Czechago) was more about thumbing the eye of the anticommunism of the West, it was not a celebratory picture of the USSR, especially in contrast to how the "Old Left" romanticized the Soviet worker state.

The transgressive cultural precepts of the New Left, especially its liberal stance on sexual mores, were at odds with the social conservatism that typified Soviet leadership during the Brezhnev era. One of the odder quirks of Soviet state attitudes towards music in the late 1960s and 1970s was they felt that rock bands exemplified by the Rolling Stones, The Doors or Jimi Hendrix were a cultural plot by the capitalism to sap the revolutionary vigor of youth through an appeal to hedonistic excess. The Soviet state was very quick to repress its own counterculture whose hippies took their cues from the global movement (long hair, sexual freedom, etc.).

Writing in 1975, the German journalist Klaus Mehnert observed:

The New Left is not one of the perennial topics that Soviet writers have to write about, rather it is a marginal phenomenon in Soviet writing [emphasis original]. Therefore, it is studied only by those especially interested. Seldom have I found anyone in the Soviet Union who even knew the New Left’s name.

Menhert found that although the Soviet state published extensively about the New Left and student protests, the state was more interested in the fact that the New left was protesting than what in fact the New Left was actually saying.

Sources

Dworkin, Dennis L. Cultural Marxism in Postwar Britain: History, the New Left, and the origins of cultural studies. Duke University Press, 1997.

Katsiaficas, George N. The Imagination of the New Left: A Global Analysis of 1968. Boston, Mass: South End Press, 1987.

Mehnert, Klaus. Moscow and the New Left. Berkeley: University of California Press, 1975.

Risch, William Jay. The Ukrainian West Culture and the Fate of Empire in Soviet Lviv. Cambridge, Mass: Harvard University Press, 2011.