Yes, antisemitism wasn’t a part of communist ideology, but it was cynically used by communists to eliminate people it percieved as a threat. From Wikipedia:
During the night of 12–13 August 1952, remembered as the “Night of the Murdered Poets” (Ночь казнённых поэтов), thirteen of the most prominent Yiddish writers of the Soviet Union were executed on the orders of Stalin. Among the victims were Peretz Markish, David Bergelson and Itzik Fefer.
You’re right about local antisemitism, but was also efficiently used by communist governments. Propaganda posters from the period can be easily found on the Internet.
For a more horrible example of local antisemitism (committed in collaboration with nazis):