USSR was all about fighting for the working class rights against capitalism being inherently multicultural - so there seems to be nothing in its ideology that would go directly against homosexuality. In addition to that:
So, why then was there no gay culture in USSR, no gay weddings etc ?
I think it is like asking why drinking too much vodka was so widely accepted in the SU, if nothing in "Das Kapital" promoted it.
First, you are right that there is nothing in the Communist ideology against homosexuality. But, at the time being, there was nothing in the Communist ideology in support of sexual rights/freedoms1, neither; these ideas were popularized in the 60s and mostly in the Western countries.
Second, even if we accepted that the origin of homophobia is only religion/church2, that does not mean that once religion & church are gone then all of the people who had been receiving those teachings would be "magically" cured.
People and societies are hard to change; people who have received for all their life the message that homosexuality is evil will make that idea theirs and will keep passing it along. To fight such an "internalized" behavior it is not enough to just remove the source of the idea3, a more active approach is needed.
And third, it forgets that the people who took power after the revolution had received that same message against homosexuality through all of their lifes, too. The Communist doctrine told them to be against capitalists, kings and priests, but not to defend homosexual rights; so they did not have an ideological reason to change that.
Now, if it is that hard to change people's habits through publicity4, imagine how hard is for people to change their views about homosexuality when there were not even campaigns promoting the change.
In the 1920s there were some openings and homosexuality was decriminalized (remember, in the UK it was decriminalized in 1965), but those were far from having universal support within the Party. When Stalin (who sexually was very conservative) came to power the liberalization process stopped and was reverted (homosexuality was criminalized again in 1933). You may read more about that in Wikipedia
TL;DR Homophobia was inherited as a part of the social customs. While some in the Communist party were more open-minded, most in the Communist party leadership did have neither the ideological need nor the desire to combat this attitude, and many in fact seem to have favored it.
1The only possible exception being that of equality between men and women, and even that was still far from perfect in practice.
2To the unattentive reader: I am not claiming that, this just an hypothesis in order to avoid entering into unrelated debates.
3And again, that is just using the hypothesis that the only source of homophobia was religion/church.
4To return to the vodka example, after the revolution there where many public campaigns against alcoholism, but it remained a problem.
There were two unrelated forces that ultimately pulled in the same direction:
In a move that seems entirely unfamiliar to hard-left-wing homosexuality rights advocates in the West, USSR (and, following their lead, other Maxist based countries like North Korea) declared that homosexuality was viewed as "bourgeois decay". Quoting form Russian Wikipedia on the history of re-criminalization in 1930s:
Максим Горький на первых полосах газет «Правда» и «Известия» 23 мая 1934 года в статье «Пролетарский гуманизм» называет «гомосексуализм» «социально преступным и наказуемым» и говорит, что «уже сложилась саркастическая поговорка: „Уничтожьте гомосексуализм — фашизм исчезнет!“».[7] В январе 1936 года Нарком юстиции Николай Крыленко заявляет, что «гомосексуализм — продукт морального разложения эксплуататорских классов, которые не знают, что делать». Доклад Наркома обосновывал целесообразность уголовного преследования за мужеложство, привлекая риторические приёмы гетеросексизма: «В нашей среде, господин хороший, тебе не место. В нашей среде, среде трудящихся, которые стоят на точке зрения нормальных отношений между полами, которые строят своё общество на здоровых принципах, нам господчиков этого рода не надо».[8] Позднее юристы и медики в СССР рассуждали о гомосексуальности как о проявлении «морального разложения буржуазии».
Maxim Gorky {Famous Soviet writer} on the front pages of the newspapers "Pravda" and "Izvestia" May 23, 1934 in the article "Proletarian Humanism" calls "homosexuality" "socially criminal and punishable" and says that "a sarcastic proverb has already developed: 'Destroy homosexuality - fascism will disappear'" !".
In January 1936, the People's Commissar of Justice Nikolai Krylenko declares that "homosexuality is a product of the moral decomposition of the exploiting classes who do not know what to do." The report justified the expediency of criminal prosecution for sodomy thusly: "You do not belong in our environment, mister. In our environment, among the working people, who stand on the point of view of normal relations between the sexes, who are building their society on healthy principles, we do not need misters of this kind". Later, lawyers and physicians in the Soviet Union talked about homosexuality as a manifestation of the "moral decay of the bourgeoisie".
Similarly to what Sjuan's answer notes, these were still the same Russian people who merely 20 years ago before the revolution were, to use modern progressive lingo, radical hardline social conservative fundamentalist bigots (seriously, socially as late as 1980 most Russians were STILL to the extreme "right" of the most hardline Evangelicals in USA in everything except maybe abortion, even after decades of the Party eradicating Christianity).
They viewed homosexuality as a bad thing culturally and socially, both because it was done so by pretty much every civilization known to men (as detailed in my answer here on Politics.SE in excruciating detail, anti-homosexual sentiment was in no way unique to, or solely caused by, Abrahamic religions); but also because they were heavily influenced by centuries of Orthodox Christianity (with especial emphasis on "soulfulness" endemic to Russia).
It's important to note that homosexuality wasn't the only thing where Stalin's government made a turn-about compared to Lenin's on social issues. They forbade abortions in 1936, they abolished ZhenSovet, at some point they apparently (I can't find a good cite outside anarchist websites now) stopped co-ed education; and in 1953 Stalin was almost started his own Holocaust but died before kicking it off (and Berya promptly stopped the plans upon assuming power).
The New Soviet man embodies the archtype of Russian masculinity, which consists of complete devotion of body and labor to state. This imagery never allowed room for gay men, in a country where homosexuality was not seen as proletarian:
In the Great Soviet Encyclopedia of 1936, homosexuality was defined as “a sexual perversion” considered “shameful and criminal.”... The persecution of gays under Stalin was no mere recrudescence of traditional bigotry, however. Homosexuals were regarded as “asocial” outsiders, and therefore potential subversives, potential threats to the new system, which aimed at total control. They were also a threat to the super-productivism mandated by the drive for rapid industrialization. Soviet industry demanded ever more workers, while the maximum diversion of resources toward armaments and capital goods meant that the traditional heterosexual family had to assume the bulk of the cost and burden of maintaining the labor supply.
Also add -
All of these were present, pervasive, and repressive.
In an era where purges, disappearances and shunning were living memories or realities, and where a job and house depended on whether and how good a citizen you were, they would have had added weight and pushed others to show intolerance, in order to show they were good.
It requires a deeper understand of the communist model of the Human. Similarly the nazis, also the communists had an idealist model of the human.
The main critics against the communism is that it is not possible, because people requires typically strong motivation to be a cooperative and not a parasitic member of the society. In our current world system, this motivation is the money. The sad truth is that most of us wouldn't work, or would work much lesser or much different, if we wouldn't need to get money.
The idealized "socialist human" works because he wants his society to get to the communism. In the communism, they work on their ideals, and all of the dirty/unpopular work is automatized.
It is not true that the communists had false dreams, they knew this disadvantage of their ideals very well. Their idea of the communism also contained, that to reach this perfect society, also the humanity has to develop to a point which is compatible with it. Furthermore, they hoped to solve this essential problem by automation and industrial development, but also with the development of human race.
See that sculpture. Man and woman, symbolizing that they work together. Their position shows as if they are being part of a large, heroic battle, and that they are fighting this battle not with weapons, but with tools. With sickle, and with hammer. (The sculpture has also the secondary meaning, that the workers and the peasants are working together, in such a close cooperation like husband and wife.) It was also the coat of arms of the CCCP. The sickle and the hammer in its coat of arms, are the same sickle and hammer, as you can see on the sculpture:
In our current society which is likely governed by an idea to make the humans worser, but happier and equal, homosexuality is accepted, even encouraged by the ruling ideology, the liberalism. But it is not "natural development" of the modern societies, if you see the world history, you will find only a few of them who followed the same line and survived at least centuries after that.
Homosexuality was not a central point in it. They disliked it, but not because it had been a central point of their ideology. They disliked it because they wanted to create the perfect, "socialist human", and homosexuality is at least a sickness, a degeneration, far from the perfection.
This "socialist human" had also only a single wife, they had sexual relations only in the marriage, but against the non-planned parenthood advised by the religions, they had lived in a perfectly planned family model, in which the man and the woman are equal and both of them work.
In their view, homosexuality was a degeneration from this model, but it was not a central point. The central point was that they are atheist, egalitarianist and they work on their best skills as well-oiled pieces of the larger machine: the communist state. And, in exchange, they get from the state as they only need.
They had been also atheist. Some religious directions did exist in the communism, for example, Christmas had been changed in the Sovietunion to 7th Nov (the largest national holiday of the CCCP, the anniversary of the "Great Socialist Revolution"). Or Lenin had a mausoleum where everybody could wonder on his dead mummy. But, what is very important: these, quasi-religious practices were in theory not religious. They didn't imagine any "spiritual power" to Lenin's mummy or to their certificate of membership in the communist party, they had considered a terrible insult, that these are essentially religious practices (and, in some eras and countries, for example under Stalin, such a statement could have leaded from prison term to execution).
Making the communism friendly to the homosexuality, it hadn't been an essential change. They were hostile to that, because their era existed mainly before the current, liberalist world and as the world history shows, being a society tolerant to homosexuality and its century-long survival are mainly opposite things.
While SJuan76's answer is good, there's a deeper question which seems to have gone unanswered. We understand that Soviet societies did not have equality movements, as happened in Western Europe, like gay rights. And we understand that Marxism is primarily about class conflict, and so everything else tends to be overshadowed.
However, why then does society default to such a position? Why did Russian society default to an older prejudice?
One of the most insightful works of political science is the Inglehart-Welzel Cultural World Map. Inglehart and Welzel attempted to classify national cultures by using two axis: Traditional vs. Rational-Secular, and Survival vs. Self-Expression. This chart allows different cultural groups to be defined, Ex-Communist is one such group.
Amongst Ex-Communist peers, Russia has the strongest emphasis on Survival values, in direct opposition to Self-Expression. To put this in context, Russia ranks higher on Survival values not just compared to most Ex-Communists, but also almost every other national group, from English speaking to Latin American and even African.
The authors of this graph have said that the results cannot be explained just by economic circumstance, though that certainly is a significant factor. In Russia's case, exceptionally survivalist culture seems to owe a lot to relative poverty and history.
Russia's national circumstance is a prisoner of geography. Russia's heartland is flat, surrounded by vast distances of flatness completely lacking natural defences. This has meant that Russia's borders have been hard to defend, and the Russian people have suffered many wars. Each of these wars has been a fight to the death, and a battle for the very survival of their culture.
The existence of the Soviet Union was never a given, and since its inception it has had to fight to survive, first in the Russian Civil War, then in the Second World War, and ever since it prepared for a war with America. This context leaves little room for self-expression.
Prejudice against homosexuality must be understood as part of a larger pattern of survivalist values. For example, the Mother Heroine medal, awarded first in 1944 for women who had ten or more children, and discontinued only due to the collapse of the USSR in 1991. The individual's hopes, dreams, feelings, opinions, are irrelevant in service to a totalitarian system. Love and sex exist as a means to provide for and thus empower the collective. Those who do not comply are recognised as subverting the authority and thus power of the state. When everyone is conscious of existential threats to collective survival, any behaviour to the contrary is regarded as threatening selfishness.
