The organization was dominated by Moscow and the Kremlin, but contained much of Eastern Europe. Did Poles, Ukrainians, Latvians and the like consider themselves to be conquered by Russians, or just one part of a broader and equal whole? I'm more specifically asking about Eastern Europe rather than Central Asia.
First of all, apologizes for the belated response.
There was not substantial “anti-Russian” sentiment in an ethnic sense. While ethnic Russians did dominate most of the top political and military positions, save for some notable exceptions such as Stalin and Beria who were both Georgian, there was not a widespread hatred of ethnic Russians. There was however widespread anti-Soviet sentiment in Eastern European countries from 1917-1991. This resentment against the Soviets stemmed from the many atrocities the Soviet government committed against the populations of Eastern Europe. I’ll highlight some notable examples of this anti-Soviet resentment (other than these nations asserting independence in the late 80s/early 90s).
Before doing that though, let’s start with a brief history of relations between the nations of Eastern Europe and Moscow. Estonia, Latvia, Lithuania, Ukraine, and Poland were all part of the Imperial Russian Empire and each took advantage of the political upheaval caused by the Bolshevik Revolution. Ukraine’s bid for independence failed in 1921 and Ukraine would remain as one of the (eventually) 15 Republics that made up the Soviet Union until 1991. Estonia, Latvia, and Lithuania each made successful bids for independence and spent the 1920s and majority of the 1930s as independent nations. This changed with the Secret Protocols portion of the 1939 Molotov-Ribbentrop Pact between the Soviet Union and Nazi Germany. In this agreement, the German government ceded influence over the Baltic States to the Soviet Union, who established puppet regimes in each one before incorporating them into the Soviet Union as Republics. Poland, whose independence was guaranteed by the United States after World War I, never became part of the Soviet Union, save for the area annexed by the Soviet Union after the German invasion in 1939.
The atrocities committed by the Soviets in Estonia, Latvia, Lithuania, Ukraine, and Poland were the main cause for anti-Soviet sentiment. 3.3 million Ukrainians died in famines in the 1930s. While Ukrainian farmers starved, Soviet officials collected Ukrainian wheat needed for export. When eastern Poland was annexed in 1939, the Soviets murdered or imprisoned Polish politicians, members of the Intelligencia, and anyone else Moscow deemed politically unsafe. The most famous example of this is the Katyn Massacre. The Soviets did the same in the Baltic nations in 1940.
Other than independence attempts in the beginning and end of the Soviet era, World War II provides some of the best tangible examples of anti-Soviet resentment. When the Germans invaded Ukraine, Estonia, Latvia, and Lithuania, many viewed the Nazis as liberators. Ukrainians quickly learned that German atrocities would be on par with what the Soviets had done. Ukraine suffered large scale military action, the holocaust, and murder of its population by the Nazis during the Second World War. Despite this, some Ukrainians did join German military units, but more would join the Red Army when the Soviets began retaking Ukraine later in the war. The non-Jewish populations of the Baltic nations did not suffered the same fate as many Ukrainians. Therefore, there was a higher degree of collaboration with the Germans. Estonians, Latvians, and Lithuanians joined Waffen SS units made up of their fellow countrymen and these units fought against the Soviets on the Eastern Front. Additionally, an anti-Soviet partisan group known as the Forest Brothers continued their guerilla campaign against the Soviets in the Baltics until the mid-1950s. Similarly, in Poland the Polish Underground waged a guerilla war against both German and Soviet forces, until destroyed by the Red Army in 1946. In all of these countries, after the Soviet Union drove out the Germans, the NKVD (Soviet Secret police) rounded up and executed or imprisoned those that support anti-Soviet efforts.
All of these efforts to resist Soviet control failed. Ukraine and the Baltic nations remained in the Soviet Union until 1991 and Poland spent the majority of the Cold War controlled by a puppet government. The Soviet Union kept a large military presence in each of these nations, and demonstrated in 1956 and 1968 that it was willing to use its military to stop domestic unrest. In the 1980s, the anti-Soviet sentiments of Eastern Europe paved the way for the independence that came in 1991.
Sources: -Bloodlands: Europe Between Hitler and Stalin by Timothy Snyder -Stalin and Europe: Intimidation and Domination 1928-1953 Edited by Timothy SNyder and Ray Brandon -Postwar: A History of Europe Since 1945 by Tony Judt