I think that this was just triggered by the paranoid delusions of Stalin and his "Doctor's Plot". Not as a matter of communist doctrine which hated all religions equally.
In the early days of the party it was said, "not all Jews are Bolsheviks, but most Bolsheviks are Jews".
Fidel Castro's "anti-Zionist" campaigns beginning in the 1960s drove nearly all of the Cuban Jews to South Florida or other Latin American nations(Cuba having the largest Jewish population on a per capita basis between Argentina and the United States). The anti-semitism of the Hungarian CP following 1956 (remember that the reformer Nagy was Jewish) and that of Gomulka in Poland was partially driven by the rise of Israel but largely reflected indigenous and ideological anti-semitism as well.
As for Marxists with Israel itself, they were a factor during the period of British control, particularly in the Kibbutzim. Such folks saw Israel as eventually becoming part of the world proletariat. They were vastly outnumbered by the Social Zionists, however, and lost influence following the Soviet Union's decision to pursue a pro-Arab "nationalist" foreign policy in the 1950s.