Hey! I'm going to focus in on the 1930s and 40s to answer your question.

The Red Army from the Revolution until 1941 was largely a Russian, Ukrainian, and Belorussian institution. The proportion of those ethnicities - especially Russians - in the army never fell below 75%, and was usually much higher. This was an institutional decision implemented through a couple different mechanisms. Firstly, most Central Asian and Caucasian peoples were not subject to conscription - while they could volunteer, they didn't naturally filter into the Red Army. Secondly, the Soviet Union had a second reserve Territorial Army formed within each national/ethnic community within the country. All ethnicities would be conscripted into these bodies and carry out training and exercises a few days each month and a month or 2 in the summer.

Territorial Divisions were composed of a single ethnicity, with regiments, battalions, and companies being formed from the smaller communities. Their officers would usually be Russian-speakers from their communities, but the units as a whole would speak their native language and be composed of one national group. National military schools were also set up to train national divisions in the Territorial Army. This fit into the general ethnic policy of korenizatsiya - "putting down roots" - which meant allowing each ethnic minority to have its own nationality-dominated government, culture, etc separate from Russian-ness. The formation of national units would create cadres which would prepare the general population, perceived as "backwards compared to ethnic Russians, for general conscription

In the late 1930s the ethnic composition of the Red Army began to change. In 1935 the Politburo moved to abolish the Territorial System, gradually transferring all its units over to the regular army. In 1936 the draft was extended to all peoples and ethnicities and at the same time the minimum age was lowered from 21 to 19. Ethnic minority national units were disbanded and their cadres gradually spread throughout the Red Army, leading to many soldiers who couldn't speak Russian being thrust into Russian-majority units across the country. Around 18,000 Kazakhs entered the Red Army in 1939 and 16,000 in 1940, compared to just 8,000 in 1938.

However, the NKO (People's Commissariat for Defense) attempted to slow this trend by delaying conscription for minorities, particularly those from Central Asia and the Caucasus. Further, at a higher level, some recent research has argued that the Great Purge more heavily targeted ethnic minorities in the Soviet command structure, leaving it much more Russian even as the rank and file increasingly diversified. In general this period also saw an increasing move towards Great-Russian chauvinism and a retreat from encouraging ethnic particularism.

The outbreak of WW2 and the disastrous defeats suffered in 1941 greatly changed the Red Army's policy towards minorities. Its preferred cadres of urban, young, and educated Russians had been killed or rendered inaccessible by the German advance. Initially, the NKO and GKO (State Defense Committee) continued to mistrust ethnic minorities, deferring "unreliable" groups such as those from the Caucasus and Central Asia from conscription, raising narodnoe opolcheniye -"people's militia" - units for local deployment, or shunting minorities into labor battalions far away from the frontlines.

This "hierarchy of loyalty" with non-Russians on the bottom served as a negative feedback loop, discouraging already unenthusiastic minorities from service. Volunteers generally numbered in the few thousands and enthusiasm for joining the Red Army was low - most people maintained a stance of apathy rather than active support or active resistance. In the autumn of 1941, facing even more defeats, the NKO began conscription for all nationalities aside from "unreliable" groups such as Volga Germans. In general, initial waves of conscription were a failure. Out of 14,000 Chechen men liable for duty, only 4,395 were recruited and 2,365 of those deserted before leaving the region. Only 28% of Crimean Tartars could be mobilized before the region was overrun. The Bashkir Republic, Turkmenistan, Kazakhstan, and Tajikistan all struggled to find recruits even among Communist Party members, and most of those they could find were Slavs who had settled in the region or evacuated there in 1941.

The NKO responded by disbanding most nationality-based units in January 1942 save for a few which had performed well or were needed for propaganda purposes, distributing the remaining men throughout the Red Army. But at the same time, responding to demands for manpower, it also ended all restrictions on minorities serving in frontline rolls - Kyrgyz soldiers, for example, were admitted to all roles starting in December 1941. This did away with all further official barriers to service for minorities. By September 1944, for example, 1 in 4 Kyrgyz had been drafted into the army.

Even when allowed to serve in the Red Army, minorities continued to face discrimination from both their fellow soldiers and their officers. Minorities were stereotyped as dumb cowardly, and useless for frontline tasks. Their often poor command of Russian made it difficult for them to bond in units in which they were minorities. In one incident in the 103rd Rifle Division, officers forced the minorities to do grunt work and dig trenches while keeping them away from important duties. In several incidents, officers would attempt to get minorities assigned to their units killed so that they could replace them with Slavs.

This led to a another negative feedback loop, where widespread abuses encouraged minorities to defect to the Nazis - according to a report from the Coastal Army in 1942, 79% of defections (A number perhaps exaggerated out of racism) were from non-Russians. "Uzbek" and other terms for Central Asians was frequently used a a pejorative for all minorities. At a wider level, minorities were frequently shunted to less active and vital fronts. For example, the largely stagnant Volkhov Front near Leningrad was 25% non-Russian in 1942. While defections did occur at a higher rate among minorities, Russians still composed 55% of defections (Compared to being 68% of those serving in the Red Army).

Linguistic misunderstanding and poor training were often at the root of issues. For example, three non-Russians were put on trial for deserting their sentry post and running away. During the course of the investigation, however, it became apparent that they had not been taught anything about frontline security and didn't understand what their job was. They were fortunately acquitted of all charges. On another occasion a Kyrgyz and Kazakh recruit were seen to stand 10-20 meters behind their comrades at the front lines. Suspecting cowardice, their sergeant had the political officer observe them. Under investigation it was found that they had never been taught to fire a gun and were trying to learn from their comrades. The 8th Guards Rifle Division, which gained renown in its defense of Moscow under the command of Ivan Panfilov, had over 20 languages spoken in its ranks. Many non-Russian recruits spoke little or no Russia and had to learn "on the job". In one amusing case, a Kazakh recruit sent to the hospital could only ask to use the restroom using swear words because of how coarse front line language was.