well, actually "conspiracy theorist" is more like a .... "under-belt-punch" (or "hit below the belt") or more particularly like an argumentum ad hominem.
(based on assumption that discrediting a person makes his argument or statement automatically "defeated" too LOL)
it is the easiest trick often employed especially by "scientists", mainstream media and of course politicians.

oh, and BTW, what's that other typical one - "Loaded Question"? ;)
like here: "you, conspiracy theorists, say that ...." - that's a very neat trick! :D
it automatically brands not only those who actually say so, but even anyone who slightly support any of those things - as a "conspiracy theorists".

talking about, trust, convincing ...
normally the "burden of proof" lies on person who accuses other party (i.e. plaintiff or persecution), not other way around (on the one who is accused). thus it is not for all those who are branded as a "conspiracy theorists" (BTW often too hastily, another fallacy of "hasty generalization") to produce the facts and evidences, but rather those who make certain statements, claiming that such and such information is "fake" (or a "conspiracy theory")

there are some online Forums and groups, like one of the most known and popular is "Above Top Secret", where a lot of people regularly do exactly that: prove fake / wrong some various information aka "debunk" it. however they do it precisely with their own FACTS - present their own sufficient proofs, not just make general branding of something what they do not like or simply can't disprove with logic, reasoning and solid facts as a "conspiracy theory" - thinking that it would automatically refute or defeat that thing.

I'm not a supporter of any "theory", but I just wanted to point out these "rules of engagement" sort of, which are a common sense in any serious enough discussion. especially since as I can see - you are well aware of the logical fallacies and try to point out when you think they are being used.

I'm not even talking about different methods of obtaining information / knowledge and accordingly those "evidences". because even so called "scientific method", based on Empirical Evidence (i.e. acquired through direct personal sense perception), is often too questionable, unreliable and most of all can NOT be used by majority of average of ordinary common people. what to talk about some other methods ...

so, what I mean is: MOST of all those subjects mentioned in this post actually beyond abilities of both sides (who may support of those and oppose too) have very little or no any means and facilities to actually prove or disprove any of that!

therefore, IMO, it is useless and may be waste of time to argue about all such things. because neither side would be able to produce sufficient evidences but only rely upon some 3rd (or even 4th, 5th .... Xth) party and practically just believe that.

well, if only may be "just for fun" ? :)