Almost 50 years later, that dream seems to be coming apart. Some of the opposition is on familiar grounds: The creationist battle against evolution remains fierce, and more sophisticated than ever. But it’s not just organized religions that are insisting on their own alternate truths. On one front after another, the hard-won consensus of science is also expected to accommodate personal beliefs, religious or otherwise, about the safety of vaccines, G.M.O. crops, fluoridation or cellphone radio waves, along with the validity of global climate change.

Like creationists with their “intelligent design,” the followers of these causes come armed with their own personal science, assembled through Internet searches that inevitably turn up the contortions of special interest groups. In an attempt to dilute the wisdom of the crowd, Google recently tweaked its algorithm so that searching for “vaccination” or “fluoridation,” for example, brings vetted medical information to the top of the results.

But presenting people with the best available science doesn’t seem to change many minds. In a kind of psychological immune response, they reject ideas they consider harmful. A study published this month in the Proceedings of the National Academy of Sciences suggested that it is more effective to appeal to anti-vaxxers through their emotions, with stories and pictures of children sick with measles, the mumps or rubella — a reminder that subjective feelings are still trusted over scientific expertise.

On a deeper level, characteristics that once seemed biologically determined are increasingly challenged as malleable social constructs. As she resigned from her post this summer, an N.A.A.C.P. local leader continued to insist she was black although she was born white. Facebook now offers users a list of 56 genders to choose from. Transgender sits on the list, along with its opposite, cisgender — meaning that, like most people, you identify yourself as male or female according to the way the cells of your embryo unfolded in the womb.

Even conditions once certified as pathologies are redefined. While some parents cling to discredited research blaming vaccines for giving children autism, others embrace the condition as one more way of being and speak of a new civil rights movement promoting “neurodiversity,” the subject of a book by Steve Silberman, published this month.