In those days, science was chiefly thought of as a framework to further our understanding of the natural world, and how we could utilize that knowledge for the betterment of our collective ends.
Societal policy and morality were issues for politicians and priests, scientists (though they did occasionally chime in). The USSR's technological progress served as a constant reminder that science was an epistemological tool, and not a teleological one.
The public was also directly downstream from the benefits of scientific advancement. Microwave ovens, color televisions, better engine, cheap refrigeration, the increasing ubiquity of plastics, and the jobs they all brought with them were conspiring to raise the American standard of living by leaps and bounds over a short period of time, and automating away many of life's greatest inconveniences. Almost every technological leap raised the tide of human experience, and every boat was lifted along with it.
Science was also the bulwark between the country, and the USSR. The advent of the nuclear bomb showed us how awesomely destructive and game changing a technological advance could be in the field of war. By the mid fifties, it was generally understood that if the US didn't have a riposte for every possible Soviet weapon, then the US could not continue to exist.
Scientific advancement was material, it was flashy, you could touch it. Rocket engines propelled humans beyond heights previously imagined, and jets shrank the world exponentially. Helicopters flew unlike anything we'd ever seen before, and even primitive computers performed mathematical calculations on their own with unprecedented speed and efficiency.
Today, science has advanced much more subtly, especially since the maturation of the microprocessor in the mid 2010s. Many of our physical advancements are refinements to technologies established in the 50s and 60s, rather than fantastical new applications of hitherto unknown physical phenomena.
Advances in material sciences and automation offer large increases in performance for industrial applications, but at the potential cost of employment, in exchange for often only marginal increases at the high-end of consumer products.
The lion's share of consumer-facing advancements in automation in particular, has been developed to manipulate, cajole, and to track our every choice. Our refrigerators remind us we need milk, our coffee makers try to protect us from unlicensed nonproprietary coffee blends. We can't share what we buy, because new technology ensures that we can only license. Every minor convenience we receive is another bar in a gilded cage being constructed around us.
More transformative advances are so abstract as to be inapplicable to the average person's life, too expensive to leveraged, or squirreled behind the closed doors of military and industry.
Scientifically sound advice for society is no longer liberating. Stay indoors, don't work. Get rid of your cars, they're bad for the earth. The words of scientists anymore often advise caution and restriction.
Science is now less often treated as a tool, and more a cudgel to justify social and economic policies. Politicians will launder their beliefs policies through lopsided studies to give their ideologies an air of impenetrable objectivity
A large handful of the population has sought to fill the existential/moral/purposeful void in their lives by looking to our scientists and technologists as if it were a new church. This is perhaps inspired by the legends of 20th century scientists, and profundities of great scientific communicators such as Carl Sagan, Michio Kaku, and Neil DeGrasse Tyson.
These people tend to be incapable of differentiating between a scientifically sound policy regime meant to fulfill goals that align with their value system, and 'the will of science'.
Others, objecting to these policy regimes, not knowing better, assume these people are right about the 'will of science', and throw the baby out with the bathwater, rejecting scientific knowledge outright, ignoring that nothing about science as an epistemological framework is reasonably morally prescriptive.
'Science says' has become shorthand for _"A group of academics or liberals want this, they think they know how they can get there, no it's not up for debate'_. So most people who don't believe in a neoliberal future ignore, reject, and sneer at the use of the term.
Through all these things, the brand of 'science' has been diluted, and tarnished to the point where much of the population no longer takes it seriously. Especially since 'science based' policies are occasionally accompanied by white lies meant to coerce people into behaving a certain way.