As was the case with the attitude of Soviet society and government toward non-white people on a public and private level(if you think racism didn't exist in Soviet society, check out what KGB analysts regularly wrote on the "national character" of the Chinese, especially after the Split), Soviet society was both liberal and conservative at the same time when it came to women's rights. One has to distinguish between public veneer for the outside world, Communist Party expectations at home, and lingering cultural norms in Russian society. Often, all three collided.

Soviet females fought as guerrillas in WWII, became cosmonauts, were expected to work. Maternity leave with generous child-care benefits and suffrage (however pointless this was in the Soviet Union) was a given, and with the exception of the Stalinist period (which had an emphasis on childbirth that would make American Religious Right figures gape in awe), abortion was available on demand. Soviet women had advanced degrees and were expected to be educated. When you compare it to where they were under the Tsars, it was nothing short of miraculous. And this did have an effect on society as a whole-as I mentioned, the Marxist experiment came in handy when it came to the fact that females were prepared to go to war in 1941. There was probably no other equivalent to that anywhere in the world.

At the same time, Russian society remained pretty conservative in other fundamental ways, in spite of the original period of Leninist experimentation in social matters. Stalin was a staunch, even aggressive traditionalist on matters such as abortion or sexual "deviance" of any kind, as alluded to above. While Khrushchev and Brezhnev were relative improvements, particularly on issues such as childbirth, they weren't exactly "feminists" either. Women still remained unrepresented in the government and were de facto paid less. Sexual harassment and worse remained endemic in Russian society. Housework and childbirth were still viewed as women's work, and women were expected to both work a day job and do all the cooking and cleaning. None of the "bra-burning" type of feminism you saw in the West was tolerated by the KGB, needless to say, and the Soviet Union in the 70s did not experience a counterpart to women's lib in the West-and that shows in Russia to this day. Women were never in practice (from a cultural standpoint) allowed to get away with vodka binging or laziness on the job as men were in spite of the official dictates, as Solzhenitsyn mentioned in his open letter to the Soviet leadership.

On a lighter note, courtship in Soviet society remained touchingly old-fashioned in certain ways. To this day, Russian guys would never think of not picking up a woman's bags for her or paying for the date and all the related stuff that you'd never see with Western guys.

To your question: the KGB and their sister agencies privately regarded a lot of the social leftist movements in West as laughable and proof of American weakness at best and deviant and subversive at worst, as Vassily Mitrokhin makes quite clear. The biggest examples of this was probably things like gay rights and political correctness in general, not feminism, but the potential of Western style feminism spreading in the Soviet Union was looked at with suspicion by the secret police. So while they were willing to boost it abroad in their foreign policy, they were always careful to make sure that it could never be imported at home. Sort of a dual face, public and private. However, many social leftist movements in the 70s took inspiration from the Chinese or Third World leftist movements rather than the Soviet Union, so this wouldn't have had as much of an effect as it once did.