More of course can be said, but this older thread is about the idea of 'race' in the USSR, and was tackled by /u/Davincier and /u/kochevnik81. It may be of interest.

This one from /u/hamiltonkg should also be of interest to you, focusing on treatment of racial minorities in the USSR.

I'd also humbly plug this one from myself which looks specifically at ethnic tensions in the Red Army in WWII.

And as simply a minor aside, Circus is one of my absolute favorite pieces of Soviet propaganda. Its really something!

Very interesting question that should be framed considering the general socialist internationalism of the era. I'd like my response to go a bit beyond Soviet concepts of race (which has been elaborated on elsewhere in the thread) and more into some of the reported experiences of non-white migrants to the USSR.

To begin with, appealing to the minds of oppressed ethnic minorities and residents of former European colonies was very high on the agenda of socialists. Both Cuba and the USSR engaged in medical and educational internationalism. According to UNESCO, based on 1964-65 data, the USSR ranked within the 'top five main contributors to the worldwide process of international education'.

The overwhelming majority of non-white migrants to the USSR were students. Between the Post-War period and 1990, around 400,000 Africans studied in the USSR. Migration from socialist countries in Latin American and the Caribbean was also common, but I cannot find any sources revealing the racial demographics of those students. Foreign students in the USSR also came from Asia and occasionally the West. So non-white people would have been a common enough site to see, especially in cities with big universities.

Prominent African Americans like Langston Hughes also travelled across the USSR and yes, the USSR did actively court Americans by juxtaposing themselves as an egalitarian society.

But what does this mean in terms of general prejudice? It's complicated to say the least. A few reported being warmly welcomed. African American musician Paul Robeson travelled in Russia in the 1930s and told reporters he felt “like a human being for the first time.” Afro-Jamaican poet Claude McKay and African American Langston Hughes were initially warm towards the USSR but later became disillusioned with Communism.

In terms of institutional racism or segregation, the USSR was not known for an explicit de jure segregationist policy like Jim Crow. With that said, the USSR had its own issues regarding ethnic minorities, especially concerning Asiatic-Russian, Indigenous and Jewish Russians. Many faced widespread human rights violations and disenfranchisement, despite the Soviet Union’s condemnation of European, South African and American racism. To this day, many Chechens, Far-East Russians suffer racism and discrimination.

Unfortunately, I do not have extensive knowledge on those areas and my knowledge is more confined to how African, Caribbean and black Americans were treated in the USSR. To summarise, for the most part it seems some degree of prejudice was common.

In Bulgaria in 1963, a clash between African students and police broke out after the African students protested the arrest of the leaders of the prohibited All-African Students Union. Many of the students alleged racial discrimination in the approach of the police, with one being quoted as saying,

“There was more racial discrimination in this Communist country than there could be in any so-called capitalist country. We are absolutely certain that this discrimination was not incidental but backed from above—by the Communist authorities."

This was seemingly appalling enough to have been raised by British politician Denis Healey in the House of Commons.

Robert Robinson, an Afro-Jamaican but American raised engineer who was approached by the USSR is an unusual case. He was exalted in Russian media as an example of an African American who had suffered racism, but later went onto document his own experiences with anti-black sentiment in Russia, which despite experiencing, claimed it was still a more egalitarian country than the USA.

Liz Johnson Artur, herself a Ghanian-Russian photographer born in Bulgaria documented experiences of black and biracial children in the USSR and for the most part many of them reported feeling prejudice and ignorant. Some reported feeling unsafe outside of Moscow.

Sources:

The USSR and International Education: A Brief Overview, Seymour Rosen

When the Harlem Renaissance Went to Communist Moscow, The New York Times

Salient: Victoria University Students' Paper. Vol. 26, No. 2. 1963.

Black in the USSR: the children of Soviet African search for their own identity, The Calvert Journal

Black on Red: My Forty Four Years Inside the Soviet Union, Robert Robinson

While in theory, the Ussr was indeed anti racism (and many sections of the government did some considerable effort to remove it from soviet society) , it is important to remind that oficial party guidelines and the influence that jingoists and nationalistics have in positions of power and influence are to diferent things, or to be more precise, were fundamental in making the soviet state what it was.

If you notice, most communist states were also coined on etnical lines (altough often pretty arbitrary ones). This sort of path was decided during the 1920s, when Lenin more idealistic aproach for a european socialist confederation were dropped in favour of Stalin more centrered one. The point that I am trying to get is that, the USSR, despite oficial guidelines, was more than anything else a ''slavic'' socialist republic, to not say a russian socialist one, which in many ways continued and resembled the original geopolitical and culturals paths of old russia nationalism and geopolitics. It is hard to deny: from russification policies (which often showed to be more brutal than even imperial russian ones) to straight up ethnical cleanesing helped shape the way the comunist state in a ''russian'' manner.

basically: the nationalists that existed trough russian history, were also the ones who participated in the creation of the soviet state.