The USSR produced propaganda like this and this about the plight Black people faced in the States, but what did the regular USSR citizen know about the civil rights movement? If I went back to 1970 in the streets of Moscow and asked a person if they knew who MLK, Malcom X, Rosa Parks, or Emmit Till were would they know?
(For ease of understanding, let us remember the descriptors of a few key terms in their context-- communism as the eventual, inevitable, ideal state espoused by the USSR; capitalism as the American understanding of its own opposition to the USSR; negro as the term used at the time. Okay, let's go!)
The starting point for Soviet understandings of race relations in the USA, as with so many discussions of Russian belief, must begin with a dark joke:
A U.S. car salesman asks a Soviet counterpart how many months the typical Soviet citizen must work to purchase an entry-level car. The Soviet pauses and contemplates for a moment, before answering: “Well... In your country, you lynch Negroes.” [x]
Or, more in the joke format, you can hear from the President of Czech Republic in 1980:
American: Your subway does not operate according to the timetable.
Soviet: Well, in your country you lynch Blacks!
Commonly described as "and you are lynching negros"/"and you are hanging blacks," it became a shorthand for Soviet criticism of American conduct. The phrase in Russian (А у вас негров линчуют", A u vas negrov linchuyu), is considered by many (notably non-Russian) sources as an example of whataboutism-- i.e., how dare you presume to criticize me when you have your own issues. It's kind of a game of ping-pong: America criticizes the USSR for its treatment of Jews; USSR criticizes America for its treatment of black people. Israeli, American, post-Soviet, and British sources commonly describe it as whataboutism.
However, the phrase is important beyond political discourse and Soviet joke history, because it also speaks to the Soviet understanding of America's structures and its failings.
Initially, the "joke" was used as early as the 1930s, when the USSR used the discrimination black people suffered in the USA as evidence of the country's inferiority: the failings of capitalism and the hypocrisy of American discourses on liberty. The Statue of Liberty is featured in propaganda like you've shown to maximize the America/irony.
When mass media became more widespread in the 1960s in the USSR, the power of the emergent Civil Rights movement made highly effective anti-USA propaganda. It was proof positive that America was failing-- and could be spun a variety of ways. Black people could be presented as a working class, beaten down by American tyranny and capitalism; black people could also be presented as an underclass of people, which the purportedly mighty American state couldn't keep "under control."
It's worth noting that Africans living in the USSR, along with non-white Soviets (Turkic peoples, mostly) and Russian Jews suffered significant discrimination. The official state policy of the USSR was ethnic unity and non-discrimination but it wasn't practiced as such. Again, the plight of the Refuseniks (Soviet Jews refused their right to emigrate to Israel) was deferred with the "lynching negroes" comments. Some Soviet publications would have mentioned major civil rights uprisings in the USA (provided they were unflattering.) Additionally, their intended target with pro-black materials was probably with nations sympathetic to the USSR/anti-USA in the developing world, rather than black people in America: Angola, Ethiopia, Uganda.
However, it is unlikely the average Soviet would have been aware of key figures of the civil rights movement. Scholars, yes, but for the average person, the Soviet news engine didn't work like the media we have. By the mid-1970s, Soviet scholars at major universities were preparing dissertations about black nationalism [x] and the works of more radical black figures-- Malcolm X, for instance. It didn't hurt that some of his views meshed nicely with Soviet ones: "you show me a capitalist, I'll show you a bloodsucker" required no edit but a translation.
News media in the USSR was used in support of political aims exclusively. (I know the word propaganda is thrown around a lot, but consider its meaning formally: all media owned by the state to serve state ends.) If a detail wasn't going to be used in support of embarrassing America or providing evidence of inferiority, it likely wouldn't be repeated with much enthusiasm. Remember that in states with incredibly repressive control of people, making a hero of an ordinary woman fighting against the law could unintentionally damage narratives of control. Rosa Parks represented a broken America, yes, but she also represented the power of ordinary citizens to overturn the law with civil disobedience. You can imagine how that might make a Soviet official shudder.
Consider MLK, known of course for his now-mythic stances against American racism and discrimination. Sounds good for an anti-America machine, right? However, he proved a problematic figure for the USSR given his religiosity and the fact that he specifically did not endorse communism:
Evolution, rather than revolution... is the most sane and ethical way for social change to take place. This, it will be remembered, is one of the points at which socialism differs from communism, the former [strikeout illegible] emphasizing evolution and the latter revolution. Communist would insist that the means justify the end. So if killing a thousand people will bring about a good end the act is ethically justifiable. It is at the point that I am radically opposed to communism. Destructive means cannot bring about constructive ends. The mean does not necessarily justify the end, for, I would insist that the end is pre existent in the mean. [x]
All of this is to say: the USSR exploited American racism-- with the goal of shining light on American flaws.
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