The general public is skeptical of scientific endeavors simply because they don't have an understanding of where mankind is at from a science and engineering standpoint. They can't understand how it would be possible to actually put someone on the Moon and so they assume that since they can't understand it -
no one can. Hence the conspiracy theories.
Right here where I work we accelerate negatively charged hydrogen ions to about 90% of the speed of light, strip the electrons off to leave only the protons, pack these protons into bunches of about 1x10^14 protons each and then fire these pulses of protons at a liquid mercury target at a rate of 60 times a second to produce neutrons that then get moderated by liquid hydrogen. Pretty much every step of the process is outside the understanding of the general public (most present company excluded, of course
) and yet we do it every day...