In my grandfather's day, only a "Russian" could get a degree in Russia. Not a Mennonite (which he was), nor a Jew nor any other group - just what they termed "Russians". He was refused his degree because he was Mennonite. Mind - his home town as well as all the other communities in the area were purged in the 1920s and we get stories like "Fiddler on the Roof" from that area.
fwiw: his hometown - all of it that I know of - ended up in Manitoba - because he hauled them out on ships. (it's a complicated story. There's a couple of books out about it). If you want to know more, investigate into the Ukraine area and how Jews and Mennonites were treated, 1880s through 1900s as well as 1920s.
I don't know when they started allowing Jewish people degrees in the USSR, but I'm going to guess it was probably post-Stalin.
on the flip side, my grandfather was also very antisemitic. My grandfather died long before I was born - and he tried to get his degree in the early 1900s, so this isn't modern information by any length.