Yes, Stalin killed people of all backgrounds. But so-called reactionary nationalities were specifically targeted for NKVD operations. For example, the NKVD would round up people with Polish-sounding names from telephone books during the Great Purge. Entire peoples were deported to Central Asia—you can't deny an ethnic dimension to his Terror.
Whatever Stalin's initial intentions were for the Doctors' Plot case, it ended up taking on a clearly antisemitic character, with the media hyping up the threat of Zionism. We may note that while Khrushchev denounced the Doctors' Plot as having been fabricated by Stalin, he didn't denounce the antisemitic rhetoric.
As far as I know NKVD did not massacred Jews. A few dozens arrests and closed elite universities does not really compare to tragedies of other nations (hint: I am Polish).
My point is that there were instances of Jews being discriminated against in the Soviet Union, and in the case of the Doctors' Plot, even being targeted in purges. I agree that many other nations suffered far worse under the Soviet regime, though the Soviet Jews obviously suffered much more under different hands during WWII.
Anti-Zionism is not antisemitism, but when Anti-Zionist rhetoric is used to condemn anyone with Jewish names, that sounds pretty antisemitic to me.
Whatever Stalin's initial intentions were for the Doctors' Plot case, it ended up taking on a clearly antisemitic character, with the media hyping up the threat of Zionism. We may note that while Khrushchev denounced the Doctors' Plot as having been fabricated by Stalin, he didn't denounce the antisemitic rhetoric.