"the people"'s attitudes to "science," in my experience of 30 years in the trenches of Big Funded Science, vary widely from near-religious awe and worship, to gee-wow kidlike fandom, to patriotic/nationalist fervour, to complete indifference, to suspicion, to active hostility, to cargo-cultism... and more than one of these attitudes can be found in the same person at the same time, moreover.
it was much easier for the public to relate to science as an activity in an era of more basic discoveries from more easily-obtained data; we are way out on the edge of the diminishing-returns curve here in primary research, not necessarily in the value of the results obtained but in the amount of effort, complexity of concepts, and cost of equipment needed to do most original physical science in our time.
the mathematicians have it easier, they only need their brains and occasionally some serious compute power... for most of the rest of us techne-based science workers, the cost of the tools is getting ridiculously high and we are definitely in the Age of Didactic Machinery here: the tools are complex, precise, and frail. this makes the "frontier" of research very, very far from the kitchen chemist or backyard astronomer; an average person's hope of replicating any of our results or being able to contribute to the field (in terms of primary data gathering) is about nil, and not surprisingly this makes science a kind of "pro sport" which people observe from a far, far distance rather than doing themselves.
opensource sharing of primary datasets might change this considerably; 10 million bright people mining the collected astronomy data of the last 30 years, with ubiquitous cheap compute power and dataviz at their fingertips, might come up with several original and valid insights from outside the academy. that would be a fine thing, and the VO gang are working towards it.
back in late C19, doing science experiments at home was very popular... cool stuff you could do with an egg and a bottle, that kind of thing.
as to the cargo-cult aspect, far too many people shrug their shoulders at planetary resource limits, reciting "scientists will think of something" as they get back into their SUV. this blind faith in a fetishised Science is imho another product of the distancing of the well-funded frontlines from the public.
scientists would also do well to remember that it was scientists who promoted the toxic chemical agriculture that now turns out to be a global threat of great magnitude; scientists invented the A-bomb; scientists promoted DDT and Thalidomide, perfected napalm, and contributed to many another minor and major disaster. legions of scientists work in the war/weapons industry. and scientists spent millions and billions on projects like space shots, while poor people in the US starved and died of preventable diseases and so on. ("Whitey's on the moon," as Gil Scott-Heron memorably quipped). people tend to remember these things.
we can take each of those instances and deconstruct it to show how commercial interest (profit motive) or military nuttiness or politics warped the scientists' ethics or prevented good science from being done; but successful scientists, like successful politicians, work very close to very large pots of money and have, alas, often been corrupted or at least paid to shut up. the ideal of science is total honesty and total glasnost, but like the ideal of American democracy it has often been honoured more in the breach... and people remember that. they have many memorable reasons to generalise that scientists have sone serious ethical boundary issues and are far less interested in the public welfare than in their own careers.
I personally think -- cf earlier remarks on credentialling and professionalisation -- that we ought to stop calling it Science -- as if it were a separate, special, higher-status activity than other activities that are useful to our survival -- and start distinguishing science that is survival- or sustainability-oriented, serves the common planetary good, from science which is grandiose, not cost-effective, authoritarian-oriented, serves to entrench the power of elites, etc. why should we draw a distinction between "scientists" and "communalists" as if they were opposites? to be anti-communalist at this point in our understanding of climate, biolology, energy, etc. is essentially to be suicidal or murderous or both. to be anti-science today, in the sense of being in denial about the laws of thermo or the meaning of "finite," is also suicidal and/or murderous. why shouldn't scientists be communalists? why shouldn't communalists be scientists?
imnsho there is no reason to believe that people who are not scientists are somehow reason-disabled, or don't understand the scientific method (empiricism, repeatability, refinement). carpenters, farmers, plumbers, contractors, mechanics, bike trailer designers, fishermen, cooks, and everyone else who actually makes something or does something uses "the scientific method" as they solve problems and learn what works and what doesn't. the degree to which we use mathematical modelling and high-tech instrumentation is the primary difference between "scientists" and every other kind of problem-solver. scientists have no copyright on the empirical method, they just like to claim one :-)
it is also imho an elitist and unfounded assumption to believe that only scientists have an orderly or widely communal body of knowledge. collective wisdom, documentation, and multigenerational experience is also passed down to people pursuing all kinds of other trades/activities/hobbies. the tone of some of the remarks earlier in this thread suggest to me an unexplored reason why some of "the people" don't much like scientists; many scientists think that their chosen trade makes them a kind of aristocracy, naturally superior to others whom they look down on as some kind of lumpen inferiors. this is not an attitude calculated to win friends :-) the elitist attitude is most clearly reflected where scientists (warped usually by big money) inflict undocumented and undiscussed risk/damage on the social and biotic fabric, as in the uncontrolled and irresponsible release of GMO and other examples mentioned above.
another thing to remember is that science follows ideology just as religions follow ideology; although vindication usually comes along eventually for positions that were politically unpopular but scientifically valid, it usually comes along a generation or two later -- after the mandarins of the previous paradigm have died, not changed their minds :-) the scientific establishment (and that ought be an oxymoron of sorts right there) has a patchy track record at best for the kind of enthusiasm for and openness to new insights which, ideally, ought to be the heart of the scientific culture. inside the world of science, we all too often do not practise what we preach... The difference between theory and practise in practise ...