Right, I should have been more clear. I've spoken to these folks not trying to change their minds, but to attempt to understand human psychology better.
Among the various large scale conspiracy theories out there, flat eartherism has, in my opinion, some useful properties.
Did the US Government fly missiles into the world trade centers? No...but proof to the contrary isn't trivial.
How can I prove the world is round? Well, it costs some money, but it's trivial. At the moment, Air New Zealand 30 is flying direct between Auckland, NZ and Buenos Aires, Argentina. The flight time will be just under 12 hours. The aircraft is a Boeing 777-200ER. This is a fast flying aircraft, but it's not supersonic, which it would have to be in order to fly between NZ and AR in 12 hours across a flat earth.
Almost anybody with a few thousand dollars can conduct this experiment.
So, I have studied flat-eartherism as a way to study some fundamental natures of human thought.
I've run into true believer flat-earthers who were intelligent, (mostly) open minded, charismatic and curious.
I think that every human brain is packed with irrational beliefs and thoughtful fallacies. Even the best, most clear thinking of us is, I believe, saddled with (nearly) unbreakable irrational thought processes. For most of us, they're not very obvious.
This isn't an implicit call to give up on the goal of embracing rational thought in all things. Far from it. For me, at least, understanding that I have such weaknesses hidden inside is an even stronger motivation to do everything possible to think and act clearly.
She's not spouting this because it's rational.
If there's anything I learned from my experiences in organized religion, the skeptics' society, various mental institutions and a career in criminal justice, it's that confronting irrational targets (or salesmen!) just teaches them how to better-reinforce their own flawed arguments and behaviors. They learn what rational people will come at them with and learn how to counter or subvert it, which helps them become even more persuasive to their next mark. Now they sound more intelligent and authoritative, which is precisely what makes them so dangerous!
The same advice applies to internet trolls. It's hard because it's instinctual, but never engage-- smile and walk away. Don't give them an opportunity to learn how to exploit or undermine the thought patterns of a rational person. If you don't yourself drown in their sea of circular logic, you're just giving a malicious organic learning algorithm free training data at the expense of your time and sanity.
If you starve them of attention, they can only feed off of each other-- to predictably amusing ends. Without outside input, then like any cult, they eventually become an incestuous feedback loop of lunacy that deviates so far from societal expectations of normality that you no longer have to convince anybody of anything since they do it for you.
It's true that I generally don't engage with people who believe in a flat earth or who claim to be absolutely certain that the government is colluding with extraterrestrials, simply because I doubt any good would come of such an interaction.
IMO that excludes all flat Earthers, at least those who have received a primary school education.
Dehumanizing or disrespecting others is one of the easiest dangers, as is challenging with a incomplete or fallacious counter.
These only add fuel to the fire.
Even if they don't, who cares? By virtue of being a flat Earther you basically exclude yourself from any position where such a viewpoint might be relevant. They're not hurting anyone, so just leave them alone. Let people be wrong on the internet.
(Note that like many aspirational exhortations, this one is a little hypocritical. I've been known to have a problem with people being wrong on the internet before. But I'm trying to be better. :))