Well this is difficult to answer. Are you referring to the antisemitism of the Soviet people or of the Soviet government? Officially antisemitism was illegal in the Soviet Union however due to the nature of the Communist state public religious worship was severely restricted. Zionism has a complex history in the USSR also with Stalin initially supporting it and later taking an anti-Zionist position.

I wrote a research paper on the refusenik movement for an undergrad class. Since I'm at work I don't have access to it but I can check my sources and give a more detailed answer later today. It's a fascinatingly complex issue.