Population growth in the mid twentieth century was an existential threat to humanity, similar to that posed by climate change today.
But the conclusion "Population growth went away, therefore climate change will also go away" is nonsense - neither problem can be solved without direct action to solve it.
There are only two possible outcomes for a world in which population is growing exponentially. Either lots of people are going to have to die, or people are going to have to have fewer children.
Similarly, there are two possible outcomes for carbon dioxide emissions. Either lots of people are going to have to die, or people are going to have to burn dramatically less fossil fuel.
In the 1960s, the received wisdom (from mostly male anthropologists and demographers) was that women wanted large families, so only totalitarian measures to reduce family sizes could prevent ongoing population growth.
Today, the received wisdom is that people demand fossil fuel energy, so only totalitarian measures to reduce energy use can prevent carbon dioxide emissions.
Both assessments missed a vital technological solution.
It turns out that educated women, on average, don't want large families. They had large families, because they didn't have access to reliable and effective contraception. The population bomb was defused by the invention and development of the oral contraceptive pill, and population growth is now limited to places where access to the pill, or to good primary education for girls, or both, are absent.
Similarly, we have a technological solution to carbon emissions that doesn't require a mythical population of people who like living without large amounts of energy that is reliable and consistent (and, vitally, isn't affected by extreme weather).
The existence of a technological solution isn't sufficient; We need to see a demand for it, so that it's widely implemented.
The idea that "population growth was never a real problem, people just got really panicked over nothing" is nonsense. Population growth was an existential threat, and it was only the wide adoption of a technological solution that averted that threat.
Climate change is also an existential threat; We need a massive program of replacing fossil fuel energy with nuclear fission energy to avert this threat.
There are still many people today who, oblivious of the demographic impact of the oral contraceptive, are terrified by population growth. Those people are worrying about a non-problem - but their predecessors who were worried about the same problem back in the '60s and '70s were right to worry, and mostly missed the fact that a technological solution had already been demonstrated, and just needed wider use to resolve the whole issue.
There are also people who are oblivious to pretty much everything, and who just know that population growth went away without them personally doing anything, and that therefore climate change will similarly go away without anything significant changing in the world. These people are dangerously uninformed.