I am originally from central Russia and I've learned about anti-Semitism in Soviet Union only after moving to US. Yap, never heard or witnessed anything like that while living there.
Another interesting thing is that several of my Jewish friends told me that their parents asked them to lie about anti-Semitism when they were interviewed at the US embassy in Moscow in the late 90s.
In the 90's, most of jews packed their things and promptly moved out. Same for a million "germans" who last were to Germany five generations ago.
But russians were stuck, nobody wanted russians (other "mundane" people of Russia, too). I wonder if that's also racist.
2. I suspect it is due to the US government. We really don't want communists in our country. Source: my partner and I immigrated from different "communist" countries.
PS: To put the OP in context (not to condone the practice in any way), the discrimination was directed not just against the Jews, but more generally against any graduates of a select few top specialized physics/math schools (most had over 50% Jewish students). From what I understand, the driving factors behind the discrimination were along the lines of: These schools at the time (70s through mid-80s) were viewed as disloyal; their graduates likely to emigrate to Israel/US post-graduation, overrepresented at top programs etc.
eg the Doctors plot https://en.wikipedia.org/wiki/Doctors%27_plot
One non-Jewish person claimed there was no anti-Semitism. Everyone wanted to escape the Soviet Union and people just resented Russian jews because it was easier for them to leave. So I thought maybe anti-Semitism is so engrained that they didn't even notice it. Kind of like how some white Americans don't believe racism exists.
[1] https://en.wikipedia.org/wiki/History_of_the_Jews_in_Russia