> Why should I — someone with many of my subjective ideas and opinions try and talk someone else out of their personal beliefs and opinions.
Because letting people operate on a false belief affects everyone else.
It's one thing to believe in homeopathy as curative - it's another thing to recommend it to people as sound medical advice, when there is no evidence that supports it.
It's one thing to personally believe in creationism - it's another when you insist on teaching it in schools, disregarding its empirical validity.
That's when real people, either the gullible or the vulnerable or even the ones in no position to resist, are hurt - either physically, as homeopathy can do, or intellectually, as science denial does, or even socially, as people vote against their own self-interests through an incorrect understanding of what's actually happening. You normalize this harm by allowing it to happen.
I'm not saying don't let people believe whatever they want. I'm saying it's important to insist they know where their beliefs end and where facts begin, because the alternative is them causing harm, justifying it under their beliefs, and you thinking that's alright then. Conspiracy theorists do not know that distinction between fact and belief.
You raise a good distinction between "conspiracies that turned out to be true" and "conspiracies in general", but you're talking at cross-purposes here. The article is discussing belief in clearly-false claims (as evidenced either by actual research on the subject or evaluation of the complete record), whereas you're using "conspiracy" in the classic sense of disinformation (claims which are true but where knowledge of their truth is suppressed until a later time). I would argue that, even with that distinction, the same default position to novel claims should be
assumed in everyday life: skepticism, willingness to examine the evidence against the baseline, and openness to agreeing with said evidence should it meet a strong standard. This default position usually means you don't change your current behaviour unless the evidence is insurmountable, so: trust, but verify(!!!), all new claims before acting on them, and if that verification fails, repudiate and encourage repudiation from your fellow humans.
What's important also is that most people don't have the tools to understand how to verify information correctly, so even the method above only works if you understand how to verify anything. Scientific illiteracy, innumeracy, and herd mentality are common issues here, as is cognitive dissonance or poor methodology - the Netflix documentary "Behind the Curve" describes how flat Earth experiments typically start by rejecting the premise of a globe, conducting experiments that strongly fit the narrative of globe nature, and then dismissing those results as flawed and only highlighting those which seem to indicate anything other than globe nature. That's cherrypicking, and cognitive dissonance alone lets people conclude that that's not what they're really doing. These are ordinary people, like you and I, with an impressive capability to rationalize and a reluctance to challenge whatever gives them comfort - any one of us could end up like them, in the right conditions.
That's why it's important to arm yourself too with knowledge about practical epistemology. LessWrong is a weird community, but they seem to have better resources on this than many other places, so I recommend their wiki. Knowledge of the scientific method helps, as is knowledge of the historical method. Understanding how scholarship is a prerequisite to science - that is, it's not enough to have done an experiment to be a scientist, you also need understanding of the current state-of-the-art to be able to advance a meaningful argument and to be able to demonstrate correct understanding when asked - is absolutely critical (this is the number one reason why physics and math professors receive so many emails from crackpots advocating a new proof of the Riemann hypothesis and whatnot, because these crackpots either aren't aware of the necessity of scholarship or are aware but have never been subjected to a rigorous test of their scholarship).