As I learn about the Soviet Union, I read about several things that seem to contradict the traditional ideals of communism. Mainly the inequality of the civilians. In what other ways did the USSR stray from the traditional communist roots?
The first question that you've got to ask is just what are communist or socialist principles? Given the convoluted history of Marx's influence on the Bolsheviks, that's not an easy place to start. Crucially, there is no set programme or points to work off when deciding 'what is socialist'. Even Marx’s Manifesto is more an immediate political programme and history lesson than blueprint for a future society.
I'd suggest that a fairer test is probably looking at how the Soviet Union measured up to its own ideals, which, given that they were based on Marxism, ought to be communist. So I'm going to arbitrarily do that test by taking the first few principles of the Soviet 1936 constitution and looking at the reality behind them. I've stopped after these because I'd written quite a lot and these are the most important, defining, articles.
ARTICLE 1. The Union of Soviet Socialist Republics is a socialist state of workers and peasants.
This piece of apparently boilerplate statement actually contains an important innovation that’s worth touching on briefly.
To provide context, within the Leninist framework, as first laid out in State & Revolution and ignoring a few immediate phases, a post-revolutionary society proceeds through two stages: from socialism (aka the lower phase of communism) to communism (aka the higher phase of communism). Socialism is thus the dictatorship of the proletariat (DOTP), a society in which the working class is supreme.
Before 1936 the USSR was deemed to be working towards socialism but had not yet achieved it. This was in large part due to the last part of the above clause: the peasants. Under a traditional Marxist schema the proletariat is the sole true revolutionary class and the DOTP is a workers' state. Lenin had hailed the alliance between workers and poor peasants as a necessity but one to be overcome in time, as 'peasant characteristics' fell from the Soviet state.
All of which is a long way of saying that the 1936 mention of a 'socialist state of workers and peasants' is a real break from both prior Marxist thought and Soviet experience.
ARTICLE 2. The Soviets of Working People's Deputies, which grew and attained strength as a result of the overthrow of the landlords and capitalists and the achievement of the dictatorship of the proletariat, constitute the political foundation of the U.S.S.R.
I'll touch on the nature of democracy in the USSR below but by the 1930s the role of the soviets within the USSR was fundamentally superfluous. The highest legislative body, the Central Executive Committee (TsIK), which sat at the head of the pyramid of soviets, was nominally superior to the Council of People Commissars (Sovnarkom) but in reality the relationship was the reverse. Sovnarkom coordinated the administrative work of the various ministries/commissariats while the TsIK's primary role was to provide a fig-leaf of legitimacy. And, of course, above both organs sat Stalin and the Communist Party, where policy was actually decided.
Why the soviets were important is that they were the great Russian contribution to revolutionary theory. The Bolsheviks had hesitantly adopted them in 1917 as revolutionary class organs and they'd proven central to the revolution of that year. 'All power to the soviets!' was a powerful slogan that underpinned the legitimacy of the Soviet regime.
ARTICLE 3. In the U.S.S.R. all power belongs to the working people of town and country as represented by the Soviets of Working People's Deputies.
Ha! Put simply, the Soviet Union was a dictatorship in which power lay with the party and, increasingly, Stalin. Those democratic bodies that had been central to the revolution in 1917 - soviets, trade unions, factory committees, etc - were progressively stripped of power. Elections were rigged, candidates required official approval and, as above, the soviets had no real power in any case. Progression and power in the Soviet Union was via the party apparatus, not democratic elections in the soviets.
The 1936 constitution did allow for universal suffrage and free elections and the discourse around that is interesting in its own right. However, the subsequent 1937 elections produced a stage managed victory in which the official candidates, the only ones allowed to stand, received over 95% of votes cast.
ARTICLE 4. The socialist system of economy and the socialist ownership of the means and instruments of production firmly established as a result of the abolition of the capitalist system of economy, the abrogation of private ownership of the means and instruments of production and the abolition of the exploitation of man by man, constitute' the economic foundation of the U.S.S.R.
And this is probably the most glaring example of Stalinist hypocrisy. The Bolsheviks always had a slightly ambiguous view of democratic practices but they could not deny their commitment to the welfare of the working class, an end to exploitation. That was in many ways the essence of their programme and what caused them to fall back to the NEP. Lenin was relatively clear on this point: "We must put at the heart of our concession policy the task of improving the conditions of the workers… We will not grudge the foreign capitalist even a 2,000 per cent profit, provided we improve the conditions of the workers and peasants. It is imperative that we do it."
Promises of "radical improvement in the material welfare of the workers" (Stalin) were no less routine a decade later. The difference is that the Stalinist industrialisation drive saw "the most precipitous peacetime decline in living standards known in history" (Nove). Real wages collapsed under Stalin - by 1937 they were 58-85% of 1928 levels - as workers were squeezed by production pressures, 'voluntary' bond drives and rising food prices. The housing crisis went from worse to worse and shortages became endemic - according to Filtzer, in 1948 "the average member of a peasant household in Moscow oblast' could buy a pair of leather shoes once every two years and a set of underwear once every ten". Labour laws became increasingly draconian in the 1930s, with later decrees allowing for imprisonment for being 20min late for work (Jan 1939).
Hardly the society of plenty that was supposed to mark the Soviet Union's arrival at 'socialism' and certainly something that sits uneasily with basic pro-labour principles.
Wrap-up
What you've hopefully picked up is that the 1936 constitution was pretty much bullshit. The gap between it and reality on some pretty key points was vast. Politically, the soviets were neither democratic nor held power. Economically, these were lean years for Soviet workers and peasants in which they were harshly exploited and suffered great hardship. This was a state that was not democratic, run by the workers or in which the means of production were owned by the workers.
So I'd suggest that the Soviet Union was indeed quite far from "the traditional beliefs of communism". But maybe that's just me. What is beyond doubt is that the USSR failed to live up to its own principles.
Sources
RW Davies, Crisis and Progress in the Soviet Economy
Donald Filtzer, The Standard of Living of Soviet Industrial Workers in the Immediate Postwar Period
J Arch Getty, State and Society under Stalin
Kevin Murphy, Revolution and Counter-revolution
Alec Nove, Economic History of the USSR
Jeffery Rossman, Worker Resistance under Stalin
The problem with this is, that there aren't really general Communist principles. All of them are Marxists, but Marxism only means a specific view on world history and economic history. Marx never really explained political action in detail. The Communist Manifesto only talks vague concepts.
Therefore, there isn't one real communist ideology. Marxism-Leninism (the founding ideology of the SU) and Luxemburgian thought are both equally acceptable as a communist ideology, while Luxemburg criticised the Soviet Union. And those are rather close, something like Marxist Anarcho Communism is also acceptable, but already very far away (ideologically) from the Soviet Union.
Therefore a general criticism how they weren't "communist enough" is in my opinion always a miss, and is a rather weak ideological critique, and not one stemming from analysis.
But they main point the SU was criticised for, by other Communists around the world, was that it was a party dictatorship. At latest with Stalin (mostly earlier) it shifted away from the democratic principle of the Soviet. Soviets (it doesn't have a obvious english translation) are worker councils, which in theory should make a country rolled bottom to top, grass roots. This system was subsequently abandoned and replaced by decision making from the top to bottom and the Soviets were controlled by the party and became only the appearance of democratic rule.
The thing is, the prominence given to "the party" is already written by Lenin in his earliest writings. The concept of the Vanguard party is per se open to undemocratic, authoritarian leadership. It is the thing that differs Marxism-Leninism very much from most of the other communist philosophies at the time. It is also the point where most of the criticism stems from. Understandably, as most Communists wanted to be free from economic AND political oppression. The freedom from political repression in the Soviet Union was always only a vague goal for a somewhat mythic future.
E.G. writings by Rosa Luxemburg, George Orwell or Emma Goldstein are good on this topic if you want to see what the contemporary thought was by prominent leftists.