Your post seemed to imply that the OP should accept his parents paranoia and stand aside without intervening. I'd like to disagree if that was indeed your implication. Hence my post.
When did it imply that? Did you not read the post I explicitly quoted?
1. OP was trying to figure out what to do with conspiracy theory believing parents. There were questions whether conspiracy theories are really conspiracy theories and should be questioned by OP.
2. He posted, in context of #1 that certain facts, like "earth is flat" is verifiable.
3. #2 is the post you explicitly quoted, and questioned verifiability and interpretation of facts.
In the context, don't you think there is an implication that you are attempting to dissuade OP from #1? At least that is how I read it. What is the point of raising epistemological issues in this specific thread otherwise?
Sigh.
The OP is trying to understand "How to handle parents who believe fake news."
Unless you (and OP) think that the people in the OP are completely irrational and insane -- in which case a different approach is needed -- in order to make sense of any conversation you need to actually understand why people believe what they believe.
Given the OP calls them "otherwise smart people" it seems to rule out the irrational/insane angle.
Which means, people in the OP's world have a different understanding of what "facts" are. Or, another way to say it, a different interpretation of data/reality/whatever.
The problem that OP is facing is trying to understand is that from his perspective, facts are 100% incontrovertible and obvious. This means the parents (and other family) are completely irrational. But they've also said they are, and I quote, "otherwise smart people."
It means the problem relates to interpretation of facts or even what facts are relevant. From their perspective, things make sense, which means if you legitimately want discussion vs appeasement, you have to start thinking of this whole domain as epistemological.
Within that area, there are two different types of problems. Sometimes, facts are just... wrong. Sometimes, and I think far more often it's this problem -
https://en.wikipedia.org/wiki/Blind_men_and_an_elephant - where a fact is pedantically true in isolation but doesn't necessarily lead to the conclusion when considered with the remainder of the elephant.
In that second case if you want to have productive conversations with someone who is convinced the entire elephant is the trunk, you have to acknowledge that their facts or you will never make a productive conversation. People, in general, react very quickly to not feeling validated/understood.
A lot of people can't empathize with, for example, people who think the election was completely stolen or otherwise had a lot of fraud. The thing is, there were mistakes and issues with the election. Republicans have had a field day making those issues a much bigger deal. But if you want to talk with someone on that topic, the common "there wasn't election fraud" talking line just invalidates an entire perspective that is based - at least originally - on something that both people presumably agree on.
Common ground goes a long way towards building trust, which is what you need if you actually want to change someone's belief.