I don't know that he's right (I started reading this thread thinking that he's wrong), and comparing the anti-semitism between Tsarist Russia and the USSR is probably not the right comparison either, particularly post WWII we'd expect anti-semitism to decline everywhere, so maybe it's the second derivative that we should be looking at?
The question is "would socialism/communism really help racial minorities" and for that the appropriate comparison is the same place before and after the installation of a socialist/communist state. In case of the former Warsaw Pact that is: Czarist Russia -> Soviet Union between 1917 and 1923, Second Polish Republic -> Polish People's Republic between 1939 and 1945, Nazi Germany to the German Democratic Republic between 1943 and 1945, and basically the rest of Eastern Europe in the same time frame (I'm not going to sum up every country involved here).
Also some of his arguments seem weak, for instance Jews being overrepresented in Academia: that was true all over Europe in spite of anti-semitism. I know American universities had quotas on the maximum number of jews they would allow into Phd programs, yet Jews were still overrepresented in academia. So overrepresentation in academia doesn't demonstrate a lack of anti-semitism, as we don't know the counterfactual of if they would be more over represented without the anti-semitism.
What it demonstrates is that Loss Leader's claim of Jews being systematically "denied jobs and promotions" is false. And especially that his comparison of the situation of the Jews in the USSR with black people in America is false.
Did it decline faster than it would have had the revolution not occurred? No one has asked, let alone attempted to answer that question, but it seems even more relevant. Perhaps that question can't really be answered, but we can look at whether the rate of decline in the USSR is similar to the rate elsewhere around the world and see if they kept up the the zeitgeist.
I have no answers to these questions. My prior view, based on what I've read, is that the decline was slower than elsewhere, but I don't have the data to back up that view, so I leave it to the rest of you to educate me.
Your prior view has no relation to reality. Nor is it particularly difficult to check where a country stands relatively to the zeitgeist, just compare it with its contemporaries during the same time periods.
1917
Immediately after the Russian revolution the previous government's Pale of Settlement and other antisemitic legislation was rescinded, its practice of pogroms was halted and was cracked down hard on. Legislation was introduced which made the incitement of propaganda against ethnic groups illegal. A massive information campaign was waged to eradicate antisemitism which lasted for decades, probably the most comprehensive such campaign ever undertaken by a country. And this was just in the space of few months, as for rate of change that can count.
During this time its contemporaries were having regular pogroms and massacres of Jews in Europe and of black people in the USA. Looks like the zeitgeist hadn't caught up yet to the Soviet example.
1917 - 1924
Between 1917 and 1924 3 (well, more than 3, but 3 main ones) contemporary governments ruled over various, ever-changing, parts of the territory of the USSR during the Russian Civil War. These were the Reds (the Soviet government), the Whites (the loyalist forces of the previous regime), and the Greens (nationalist forces). This also pitted the Soviet government against its international contemporaries, as the USA, Italy, the UK, France, Japan, Poland, Romania, Greece, Australia, and Canada invaded the Soviet Union in support of the White forces.
Needless to say, of course, that the legislation introduced by the Reds after the revolution was only enforced in the territories it actually controlled. During the civil war the White forces and their international allies engaged in numerous anti-Jewish pogroms and massacres, to one of which in Vilna in 1919 the US Army representative Colonel Wiliam F. Godson, present at the scene, commented that the Russian Jews are "extremely dangerous" making the "Jewish question" the most important one for the country. It took until 1924 for the Reds to repel the invaders and win against the Whites and finally end the practice of pogroms and massacres of Jews on Soviet territory, at least until 1941. Such practices, however, continued domestically in its contemporaries, both against Jews in Eastern Europe and against black people in the USA. Looks like the zeitgeist still hadn't caught up yet to the Soviet example, I'm sure it'll be right around the corner.
1924 - 1939
Yiddish became one of the four official languages of the Byelorussian SSR (a Soviet region with a high population of Jews) and the Minsk Yiddish language university became one of the most prestigious ones in the USSR. Jews became highly overrepresented in government positions and Yiddish was encouraged as a language. This policy of encouraging minority languages came to end in the 1930's when Russification started being encouraged (which wasn't an antisemitic policy change as such, it was equally true for Ukrainian or any other previously-encouraged minority language).
During this time its contemporaries in Central and Eastern Europe enacted lots of antisemitic legislation, the most well-known probably being Germany's Nuremberg laws and similar legislation throughout Eastern Europe (most notably Poland and Romania). Countries enacting such legislation (most notably Nazi Germany and the Second Polish Republic) were furthermore still supported by the West in their crusade against the "Jew-Communists." During the 1930's pogroms and massacres continued in various places throughout Europe as well the USA (from now let's make it implicit that for the USA it refers to black people). Looks like the zeitgeist still hadn't caught up yet to the Soviet example, I'm sure it'll come soon, let's try the next time period...
1939 - 1945
In 1939 the USSR took control over the Eastern part of what used to be the Second Polish Republic, rescinding its antisemitic legislation and for the first time stopping the practice of pogroms and massacres of Jews outside its own territory. In 1941, after the German invasion of the USSR, pogroms and massacres of Jews were occurring once more on Soviet territory, including the shipping off of entire groups of Jews to extermination camps. It wasn't until 1944 that the USSR was able to retake that territory ending the Holocaust there, and until 1945 when the rest of Eastern Europe was liberated. The new socialist-inspired governments in Central and Eastern Europe rescinded the antisemitic legislation of their predecessor governments and halted their practices of massacres and extermination camps.
Many of its contemporaries during that time period not only intensified their antisemitic legislation and practices, up to including the industrial extermination of Jews as a whole, and only stopped doing so through the application of sheer military might. So finally we have its Central and Eastern European contemporaries catching up to the zeitgeist, although only because they were forced to by military might, but I guess late is better than never. The USA, for its part, was still engaged in its traditional actions against black people.
PS: Strictly speaking the use of "Soviet Union" or "USSR" in the time period 1917 - 1922 is incorrect as the USSR was only instituted in 1922, but I've used the same term for simplicity.