Nietzsche famously wrote:
"God is dead. God remains dead. And we have killed him."
This quote is often used as an example of Nietzsche's nihilism but it is much more complicated. These words are actually spoken by a madman in Nietzsche's book The Gay Science. According to philosopher Simon Critchley, the quote is meant to be a descriptive rather than a normative statement. What Nietzshe was getting at is that Christianity is a religion that values provable truth and as a result of this truth seeking, science arose. Science in turn generated skepticism of revealed truth and the concept of God. Thus, the end of Christianity was built into Christianity.
Borrowing from this analysis, science may also have have a built-in mechanism for its own doom. An excellent article in this month's Technology Review describes the concept of epistemic dependence, where science and technology is so complicated now that no single person can understand all of it. In my own work, I could not reproduce a single experiment of my collaborators. Our collaborations work because we trust each other. I don't really know how scientists identify new species of insects, or how paleontologists can tell what species a bone fragment belongs to, or all the details of the proof of the Poincare conjecture. However, I do understand how science and math works and trust that the results are based on those methods.
But what about people who are not trained in science? If you tell them that the universe was formed 14 billion years ago in a Big Bang and that 99% of all the stuff in the universe is completely invisible, why would they believe you. Why is that more believable then the earth being formed six thousand years ago in seven days? In both cases, knowledge is transferred to them from an authority. Sure you can say because of science, we live longer, have refrigerators, cell phones, and Netflix so we should believe scientists. On the other hand, a charismatic conman could tell them that they have those things because they were gifted from super advanced aliens. Depending on the sales job and one's priors, it is not clear to me which would be more convincing.
So perhaps we need more science education? Well, in half a century of focus on science education, science literacy is not really very high in the general public. I doubt many people could explain how a refrigerator works much less the second law of thermodynamics and forget about quantum mechanics. Arthur C. Clarke's third law that "All sufficiently advanced technology is indistinguishable from magic" is more applicable then ever. While it is true that science has delivered on producing better stuff it does not necessarily make us more fulfilled or happier. I can easily see a future where a large fragment of the population simply turns away from science with full knowledge of what they are doing. That would be the good outcome. The bad one is that people start to turn against science and scientists because someone has convinced them that all of their problems (and none of the good stuff) are due to science and scientists. They would then go and destroy the world as we know it without really intending to. I can see this happening too.