This is only a small example but Sergei Eisenstein, a Soviet filmmaker, once invited Paul Robeson to the Soviet Union. Paul Robeson, son of a former slave, was a black American singer/actor, famous for his roles in Show Boat and Sanders of the River as well as for being blacklisted for his affiliation with communists and anti-imperialism. Though he did not live in the Soviet Union, he did send his son to school in Moscow to escape racism in the USA and took up Eisenstein's invitation, famously remarking how he had felt "like a human being for the first time since I grew up. Here I am not a Negro but a human being. Before I came I could hardly believe that such a thing could be. Here, for the first time in my life, I walk in full human dignity."

Another example would be Claude McKay, a Jamaican-American writer/poet and famous artist of the Harlem Renaissance. He wrote about his experience in the USSR in Soviet Russia and the Negro, which may be of great interest to you:

When an American writer introduced me as a poet to a very cultured German, a lover of all the arts, he could not believe it, and I don't think he does yet. An American student tells his middle class landlady that he is having a black friend to lunch: "But are you sure that he is not a cannibal?" she asks without a flicker of a humorous smile!

But in Petrograd and Moscow, I could not detect a trace of this ignorant snobbishness among the educated classes, and the attitude of the common workers, the soldiers and sailors was still more remarkable. It was so beautifully naive; for them I was only a black member of the world of humanity.

During the first days of my visit I felt that the great demonstration of friendliness was somehow expressive of the enthusiastic spirit of the glad anniversary days, that after the month was ended I could calmly settle down to finish the book about the American Negro that the State Publishing Department of Moscow had commissioned me to write, and in the meantime quietly go about making interesting contacts. But my days in Russia were a progression of affectionate enthusiasm of the peopl towards me. Among the factory workers, the red-starred and chevroned soldiers and sailors, the proletarian students and children, I could not get off as lightly as I did with the intelligentsia. At every meeting I was received with boisterous acclaim, mobbed with friendly demonstration. The women workers of the great bank in Moscow insisted on hearing about the working conditions of the colored women of America and after a brief outline I was asked the most exacting questions concerning the positions that were most available to colored women, their wages and general relationship with the white women workers. The details I could not give; but when I got through, the Russian women passed a resolution sending greetings to the colored women workers of America, exhorting them to organize their forces and send a woman representative to Russia.

This isn't entirely incidental to the culture of the USSR. In the above article Claude McKay attributed this to Russia's multi-culturalism, but it should also be noted that the Soviet Union often had pro-African propaganda and art, often in the context of attacking American involvement in opposing African liberation movements (with the Soviet Union often providing some support for such movements as well as offering scholarships to young Africans in post-colonial countries) and bringing attention to the racism in America, this is the origin of the famous saying "And you are lynching Negroes".

Above you've been linked to the story of Ivan Hannibal who was the son of Abraham Hannibal, an African slave adopted by Peter the Great, later an important statesman and also the great grandfather of Alexander Pushkin who is Russia's greatest poet. He was rather proud of his African heritage.

Source: Pushkin's novel «Peter the Great's Negro» and his diaries.

The next important group are the Afroabkhazians. They are black, they live in Abkhazia and they speak a tiny isolated Caucasian language shared only by their neighbours. Today Abkhazia is not a part of Russia anymore. De facto it is independent but from the standpoint of the Republic of Georgia it belongs to the Republic of Georgia and most of the Western nations are friends with the republic of Georgia.

There are three theories about what they are. The most prosaic one regards them as descended from black slaves imported (or having ran away) from the Ottoman empire. Maxim Gorky believed they were emigrants from Ethiopia because their placenames have counterparts in Ethiopia. And the most fanciful theory states they've been living in Abkhazia from the prehistoric era and were the original bearers of the Abkhazian language. That is based on the fact the ancient Greek historian Herodot claims that "it is plain to see that the Colchians are Egyptians" (Histories 2.104) and that they practice the same customs as Egyptians and the Ethiopians. The kingdom of Colchis was also located somewhere on the eastern Black Sea. This claim is repeated by Pliny the Elder. And of course there is this question about why the Black Sea is called the Black Sea )))

This latter theory is mired in neverending nationalist squabbles between Georgia and Abkhazia over the ethnic identity of the Colchians.

Next group are Afrosoviets. For the most part it's the descendants of African Students taken up in the Soviet Era. The Patrice Lumumba University in Moscow was founded specifically for foreign students and some it's alumni made it very far. The most widely known in Russia public figure from that group is Yelena Khanga. Her mother is Russian and her father, Abdullah Kassim, was from Zanzibar. At first he finished Oxford and then he studied in Moscow. He was leader of the Zanzibar Revolution of 1964 which displaced the Sultan but only got acknowledged by the Soviet block and by the people's republic China. USA and Great Britain replied with cannon boat diplomacy (HMS Owen, HMS Rhyl, RFA Hebe, USS Manley) and by supporting the insurgency. Yelena's father got assassinated in 1969.

There was certainly plenty of antisemitism to go around in the USSR, but the one of main premises of communism was brotherhood and cooperation. In addition, the Soviets looked upon discrimination and racism in the U.S. as being something they can capitalize on to gain the moral high ground; they saw an opportunity for them to create a society free of racial discrimination. For that reason, they erected anti-racist themes all across the USSR.

There's a book that discusses this matter in great detail actually. It's called Opposing Jim Crow: African Americans and the Soviet Indictment of U.S. Racism, 1928-1937.

It talks about the interesting phenomenon of simultaneous exclusion of blacks from political and social institutions in America, and their inclusion in those same institutions in Soviet Russia.

Now, of course, this doesn't mean that white Russians didn't harbor resentment for blacks, but it's certainly interesting to see that America's segregation was so pervasive that it spurred on the Soviets to act on it in thier own country.