The short answer is that these ideas were represented in the 60s by a small but loud minority and didn’t become less popular but rather became less visible during the times you mentioned.

Our popular image of the 60s is of hippies, Vietnam war protests, free love and general societal upheaval, however, this only every constituted a minority of people. Gallup polls found that as of 1967 only 1% of Americans had been to an anti-war protest, and only 9% would consider going to one. In a university of Michigan study asking about social groups in America fully a third of people gave war protestors the lowest possible rating and only 16% gave them any sort of positive rating. Regarding hippies A sociologist Lewis Lablonsky who attempted to analyze hippies as a subculture concluded that as of 1968 there were only 200,000 dedicated hippies in the US. This doubtless undercounted as he didn't count teenagers or people who may be hippie adjacent (for example 400,000 people attended Woodstock). And it's very hard to quantify a subculture with no hard boundaries but we can still see that hippies were not the norm for this period, and that the “popular image” of the 60s was confined to a rather small minority of people.

The popular mythos of the 60s is enduring everyone went to Woodstock, protested the war, smoked some pot and then grew up and put on a tie and went to work for the man in Nixon’s/Reagan’s America. These are almost a founding story of modern American society, but like so many founding myths it’s not really true and an idealized version of the past. And the numbers don’t bear it out there really was a silent majority that was scandalized by the counter culture rising in backlash to it. The counterculture really was a counter culture outside mainstream, even at it’s height.

The ideas of the counterculture were also not really “defeated” in the 70s and 80s rather they were organized and scattered into to many different movements and subcultures we can trace to the 60s everything from New Age Spiritual movements, to the gay rights movement had their origin there, Nixon’s silent majority was a reaction to these, and Falwell’s later moral majority the same, though by that time these ideas were no longer counter culture but part of the fabric of American society. The hippie was no longer shocking but rather a character from central casting.

Despite it’s very real cultural power; the Moral Majority/American reaction/Evangelical Fundamentalism, also has a somewhat mythical reputation, and never achieved the dominance that it sought being able to influence the political and religious spheres, but failing to gain ground in the cultural and academic spheres except among it’s own parallel institutions. Almost from it’s inception it was subject to relentless pushback and mockery. And it by no means had a lock on 80s culture as seen by the rise and popularity of music genres like Metal and laugh lines in shows like the Simpsons. While movments so such as the gay rights movement formalized and grew.

While the pop narrative is a fun one, we can see that counter culture/progressive ideas were not mainstream in the 60s and the religious right/traditional America was having trouble even at it’s height. These ideas have less ebbed and lowed than gradually shifted in one direction.

John Mueller, War, Presidents and Public Opinion (New York: Wiley, 1973), chs. 26.

Lewis Lablonsky, The Hippie Trip 2000 edition

Gallup Polling, https://news.gallup.com/poll/8053/gallup-brain-war-peace-protests.aspx