First off, everyone reading this should check out the thread the OP linked to, it's an excellent one and much better than this paltry answer.

Sexuality and the Soviet Union is a somewhat difficult topic to parse out in part because the state had different attitudes towards sex that varied over time and geopolitical contexts. Part of the problem was both the family and sexuality was something that few Marxists ever tackled before 1917. Many Marxists assumed that the problems of family life and between men and women (homosexuality was pretty far off from public debate) were the fault of capitalism's corrosive effect upon the social order. One of the few pre-1917 thinkers to give much though to the family issue was Alexandra Kollontai who argued that bourgeois morality was the root of a sexual crisis and socialism would resolve this by creating a new equitable system of companionship that would transcend the traditional marriage. However, sex-minded thinkers like Kollontai were few and far between among the Bolsheviks. Thus when the Bolsheviks took control over Russia, they found they had to implement policies regarding issues which their reading into Marx did not prepare them for, such as the family.

The Bolsheviks initially embraced an attitude that if the tsars decreed a social behavior deviant, then Bolsheviks would do the reverse. This led to the decriminalization of homosexuality, secular marriage and divorce, the end of statutory ages of consent, and the legalization of abortion. Given the unsexy (forgive the pun) nature of this work, the task of forging a new family policy in the USSR was given to the few figures that wanted to do so, like Kollontai. The latter headed the first Zhenotdel (woman's department) in the CPSU which advocated for women's equality within the new state. of course, one should not read too much into this relative liberalization of the 1920s. The state's decriminalization of homosexuality was less about accepting homosexuality than trying to create "scientific" treatments what many in power saw as a mental disorder. And the pro-sex attitudes of some Bolsheviks was intrinsically linked to politics and ideology; few of these thinkers tackled sexuality on its own terms.

Stalin's dictatorship created a more conservative attitude towards family and social mores. The state shut down the Zhenotdel in 1930 and many of those socially progressive about sex found themselves sidelined or purged. Although Stalin's more conservative impulses might have played a role in this backlash, what's more plausible is that they type of person advocating for more sexual freedoms were often typified the Trotskyite intellectuals that the Stalin turn attacked. The state became more "pro-family" as the 1930s wore on, with neonatalist policies like recriminalizing abortion. However, secular marriage remained one of the cornerstones of Soviet policy. Official Stalinist culture also became more formalized and ideological in the USSR, thus there was little room to experiment with sexuality in the new mass society. One of the things that shocked Soviet troops during the Second World War was the vast amount of pornography their German counterparts possessed when the Red Army overran German positions.

The postwar era perpetuated this stuffy culture about sexuality, with notable cracks in its edifice such as films like Moscow Believes in Tears. The Cold War certainly added a further impetus for Soviet official culture to differentiate itself from the West by emphasizing its high-mindedness and intellectualism, something Khrushchev took great pains to point out during his trip to the US. This attitude led to censorship of sex in imported foreign media, especially during the 1970s. This led to some curious cases in which the Soviet cultural guardians weighed against Western imports that were culturally transgressive. For example, Soviet cultural authorities felt that Western rock like Jimmy Hendrix or the Rolling Stones was a nefarious capitalist plot to sap the revolutionary will of youth through an appeal to sexual hedonism. Thus they begrudgingly saw disco as a safer, benign alternative.

However, the issue of whether or not the USSR was more repressed is somewhat relative. Most Soviet officials and some patriotic citizens would decidedly assert that they were not repressed and that the West was decadent. It's also important to remember that the West had similiar conservative analogues to the Stalinist cultural conservatism. The first decades of West Germany were notoriously prudish with stringent state controls over allegedly pornographic materials. Partly, this was the imperative of the CDU which inherited political Catholicism's cultural policies against Schund (trash) literature. But also like the early Bolsheviks, there was an imperative within the FRG to do the exact opposite of the previous regime. The notion that Nazism represented a perverse sexuality and sadomasochism (this is where we get the trope of the BDSM Nazi dominatrix) had some currency within West German circles and a restrictive policy on sexual education and materials was a way to correct this social malformation by a return to traditional values. Beate Uhse, the FRG's equivalent of Hugh Hefner, began a mail order catalog business by claiming what she was doing was in the interests of sound family planning and healthy marriage. Such conservative policies often found their ways into other European states as well.

A big crack in this conservative turn in Western Europe was due to the relatively open nature of Western Europe to travel and the easing of restrictions on pornography within some European countries. Scandinavia in particular became fairly infamous in the late 1960s and 1970s for its erotika boutiques. Denmark became one of the gateways for West Germans to buy pornography and the Danes would often open up shops right on the border. These Trojan horses, coupled with a generational shift within Western Europe, led to an easing of the restrictions on sexual materials. Such a process did not have an equivalent in the USSR whose leadership was increasingly geriatric in the 1970s and kept a very tight control over cultural production.

To beat a dead horse, the issue of sexual repression is relative and can vary over time. For the 1950s and 1960s, Playboy magazine was very open and progressive on sex compared to the rest of American mainstream culture, but by the end of the 1960s Hefner's publication was relatively conservative on a number of social issues. One of the consequences of the Soviet attempts to impose a hegemony over the culture of its citizens is that many of them actively craved spaces in which the state and its ideology was not present. Sexuality and sexual expression were among these spaces.

Sources

Carleton, Gregory. Sexual Revolution in Bolshevik Russia. Pittsburgh: University of Pittsburgh Press, 2005.

Healey, Dan. Homosexual desire in Revolutionary Russia: the regulation of sexual and gender dissent. Chicago: University of Chicago Press, 2001.

Heineman, Elizabeth D. Before Porn Was Legal: The Erotica Empire of Beate Uhse. Chicago: University of Chicago Press, 2011.

Herzog, Dagmar. Sex After Fascism: Memory and Morality in Twentieth-Century Germany. Princeton, N.J.: Princeton University Press, 2005.

Well, East Germany was and is historically far more open about sexuality than the West was or is, so I wouldn't say it's a capitalist thing per say.

http://en.wikipedia.org/wiki/Freik%C3%B6rperkultur#From_1945_to_present

NSFW