I agree completely that the ability to being reproducible is what makes a study or finding solid and reliable, however I wouldn't go as far as to say that anything that hasn't been replicated many times is slightly better than a lie. It might well be true but lacks robustness and scrutiny in order to be taken as a generally applicable principle (or maybe this is what you meant?).
If it walks like a duck, and it talks like a duck – you are probably not best served by making decisions as if it were a chicken.
Something hasn't been replicated many times, it is structurally indistinguishable from a lie. It might be true, just as any live might be true, but without verifiability and someone taking the steps to verify it, a clever and wise person should never use that information for judgment.
This is a much higher bar than "generally applicable principle." It is indistinguishable from a lie. This is far more insidious if it happens to be something that you want to believe.
That's the trap that a lot of these people fall into.
This is what I find most difficult dealing with: when people are shutting you down a priori because they decided that they don't trust anything that comes from science, then trying to reason and explain the evidence at hand becomes an impossible task.
I have simply taken to accepting that people who don't trust anything that comes from science have tacitly agreed that I can take from them anything that comes from science. If it doesn't exist, or it's an agency of evil, or it's an invalid way to make decisions, then clearly I'm protecting them and they should support me in protecting them – by taking their computers, their cell phones, their health, their primary, secondary, and tertiary means of socialization, the ability to move further than a swift jog…
You know, things. Derived from science. I'm helping!
Personally I don't know what the best way to deal with this recalcitrant attitude could be. Maybe your approach (which requires a lot of patience) could help to plant some seeds of real knowledge, although in my experience people like this would to anything to avoid admitting they might be wrong even if they start having doubts.
Well, there is a real and true alternative.
We could kill all of them.
It's not like they would have particularly good weapons. Comparatively. Once you toss scientific thought, your weapons development strategy goes right out the window. I'm pretty sure we could take them.
That is a lot of work, however, so I am generally disinclined to bother. In the long run, their belief system is effectively self-defeating because it demands that they take inefficient options at every turn. So ultimately, science wins. In the short term, we just have to learn how to mock them openly and without hesitation, twisting the knife whenever possible. If nothing we say can really make a difference, enjoy the performance art.