It is often repeated that during the early days of the Soviet Union people adhered to the “glass of water” theory, that held that satisfying sexual desires should be as easy as having a drink of water to quench your thirst. But was it really true for all people or only for some kind of minority? Or was not true at all, and this claim is based on some isolated anecdotes?
Well, this really is a multifaceted question. In short, it was so for about a couple of years before things normalized. Sheila Fitzpatrick's The Russian Revolution has a couple of paragraphs that assess the "glass of water" theory.
Essentially, most of Bolshevik leadership and theoreticians disagreed with the notion of free love, in so far as it was understood to be promiscuity. Now, the Bolshevik ideals did advocate for liberation in multiple ways which tied into the idea of sexual liberation. The family dynamic was rejected, being seen as a structure which was prone to instilling bourgeois and anticommunist values. This would reasonably result in a more promiscuous approach to sexual and loving relationships, since if nuclear families did not exist, women were not bound to their husbands, and so on, casual sex ought to be a natural byproduct. And indeed,
"...the glass of water approach was popular among young Communists, especially the men who had learnt their ideology in the Red Army and regarded casual sex almost as a Communist rite of passage."
What could not be ignored however was a more conservative approach by many leading Bolsheviks, notably Lenin, whose views were a tad more extremely applied later on by Stalin. In these views, sexual deviation from the traditional was, in essence, a product of bourgeois decadence and debauchery. Good communists were meant to be utilitarian, and in this way many Eastern European communists agreed: sex was primarily for procreation.
"Even Aleksandra Kollontai, the Bolshevik leader who wrote most about sexual questions and was something of a feminist, was a believer in love rather than the 'glass of water' theory of sex that was often attributed to her."
In larger cities, there was indeed a wave of cultural relaxation following the revolution, during the war, and before the USSR 'normalized'. Though disliked by many in the Bolshevik leadership, the sexually liberal subcultures were allowed to flourish, though on account of social normality, these existed primarily in large cities and as the prior quote states, in the Red Army. Though I'm not sure if it's perfectly relevant, a similar outlook towards homosexuality was seen in the more western sections of the USSR-to-be: decriminalization resulted in tolerance towards homosexuals, though this was subject of lively debate for years to come, with views being expressed from open tolerance, to it being a curable mental illness, to what I believe was the most common approach later on: homosexuality is bourgeois decadence on par with promiscuity.
It is also notable that the less socially advanced constituent republics of the USSR recriminalized homosexuality in the early 20s. This also reflects a core reason why sexual liberation in the USSR degenerated: it was a far too backwards a country with far too backwards a social structure to implement massively progressive policies. In the countryside, this was inherent, and coupled with the return to capital that NEP brought (and with it, relatively limited interference with social order, for a while at least), the radical times of the proposed new social order dissipated.
I feel the need to talk about the political elite before concluding. Though many of the Bolsheviks expressed conservative views about sex, within covert environments the party leadership, especially the Stalin clique, was, excuse my phrasing, a circle of fucking each other's wives. Alongside this, cheating with more or less random, procured women wasn't unheard of either, nor was a limited tolerance for homosexuality. Two notable figures spring to mind. One, Georgy Chicherin was an openly gay politician and one time narkom of foreign affairs, whose legacy would not be tarnished in soviet historiography. Another, Karl Pauker, was Stalin's one time bodyguard, whose covert homosexuality Stalin was well aware of. He was killed in '37, as part of the purges.
Well, this I hope answers your question. Shortening it down, it essentially goes like this: a brief liberation period after the revolution did take place, though was not looked favorably upon by Bolshevik leadership. Among the youth in the Red Army and the progressive urban intelligentsia, this sexual openness was notably common, though it died down alongside most social experimentation as society normalized post-revolution.