A. The mainstream media, M, is biased and sometimes delivers incomplete or inaccurate information. They tell $mainstream_story.
B. Alternative source, A, rejects $mainstream_story and says that actually, $alternative_story is the truth.
C. Any data M points to to debunk $alternative_story and support $mainstream_story is assumed to be fake or manipulated, because M lies.
D. There is no need to apply the same skepticism to A and their arguments, because by going against M, they have already demonstrated that they are "good guys".
This is more a form of spam filtering; given finite intellectual effort, strangers who talk about certain subjects get ruled out of consideration. Just as sending a lot of mail about Cialis will get your IP on a list.
For example, the ad hominem fallacy, where we might trust a doctor just because they are a doctor. Or when we might avoid a restaurant just because of popular opinion (bandwagon fallacy). It's strange that people would seek out these fancy words when we can just say credibility.
Similarly, we culturally expect that judges are not receiving re-election funds from the parties that appear before their court, and not because money necessarily damages their judgment, but rather for the sake of judicial credibility.
The effective judgment of credibility is not as simple as logic.
That's not an ad hominem fallacy. At worst it's an argument from authority. Ad hominem is something like: the person advancing this argument has done something bad, therefore the argument they are advancing must be false (or the converse -- the person advancing this argument has done something good, therefore the argument they are advancing must be true).
An argument-from-authority fallacy is a kind of ad hominem, usually employed with respect to some third party not involved in the dispute: "This person has a credential, and they say X, therefore X must be true." The problem is that this might not be a fallacy depending on the specific credential and the value of X. If someone is a doctor, then what they have to say about medicine is actually more likely to be true than someone who is not, all else being equal. Asking your doctor for advice on how to fix your car, on the other hand, is something you probably ought to avoid, unless your doctor also happens to be into cars.
The matter of a judge also brings up an interesting problem. The fact that a judge has financial entanglements does not preclude them from quality legal reasoning, but it does diminish their moral credibility. Would anyone say that it is an ad hominem attack to sour on a judge because of mere financial entanglement? That the legal profession would develop ethical consensus on this matter means they also believe that credibility is an essential ingredient to legal practice, and not mere truthfulness.
And on the matter of logic, that a doctor is likely to be truthful is as logical as telling a mathematician that a famous conjecture is likely true; more accurately, these are both arguments of empiricism. This is why I see insistence on terminology like "logical fallacy" to be the habit of those who enjoy intellectual ornamentation.
However, the idea of a logical fallacy is one can take an argument apart and out it back together and identify bad arguments without relying on an authority figure's arbitrary pronouncements. If one reads a restaurant review and the reviewer said they didn't like the restaurant because some hated person said they liked the food there, we can easily conclude that this is the association fallacy at work and disregard that review. If we see 1000 1 star reviews because A Bad Person said he liked the food there, and we believe it, we are falling for the bandwagon effect fallacy, by a bunch of people who believed the association fallacy.
I find there's an over-obsession with logic in some discussions too; as in, ancient-greek-style modus ponens stuff. To me, that's not particularly interesting when it comes to the real world[1]; after all, logically-speaking we could just be a brain in a jar, or whatever.
An argument being "logical" (as in, not self-contradicting) is not enough to make it credible; it's just a very low bar, which lets us dismiss the most nonsensical claims quickly. Arguments which cross the "logical" bar should also align with empirical evidence, have a likelihood that's at least comparable to alternative explanations, etc.
---
I don't think "conspiracy theory" has quite become a thought-terminating cliche yet. It can usefully describe a common failure-mode in thinking.
In particular, conspiracy theories become less and less likely as they're inspected closer and closer; e.g. requiring even more people to be "in on it" (making it less likely to be kept secret), requiring ever-more elaborate epicycles to explain-away observations/experiments/events, etc. They can't be disproved, but who cares? That's not a good enough reason, on its own, to affect anything.
Another legitimate use of the phrase "conspiracy theory" is a particular case of "affirming the consequent" (i.e. getting implications the wrong way around). For example "if X is true, Y would make so much sense", where X is the "conspiracy" and Y is some well-known/self-evident fact about the world. This might be true, but the mistake is to treat Y as proof of X: this would give us "if X is true, Y would make so much sense, so X is true", which is an elaborate way of saying 'if X is true, X is true'. Here Y isn't actually proof of anything, it's just a distraction.[2]
[1] In artificial contexts, like mathematics and programming, I find logic to be fascinating and rich; e.g. I spent a lot of time studying topics like type theory and co-induction at grad school!
[2] The "logical fallacy" here is assuming (X -> Y) -> (Y -> X)
PS: From a bayesian perspective, 'if X were true, Y would make so much sense' is evidence for X. It's not proof, but it makes X more likely (essentially by ruling-out the potential for Y to disprove X). However, (a) the change in likelihood depends on the prior probability, if X were wildly unlikely then such weak, indirect evidence cannot make up for that; and (b) this sort of nuance of probabilities is negligible compared to the wild chains of "logic" spewed by the conspiracy theorists I know.
It works like this:
A. You believe X.
B. A crazy person also believes/believed X.
C. Since you believe X and a crazy person also believed X, you are a crazy person.
D. Optionally: I won't consider your argument unless you tell me why being a crazy person is ok. Why do you support doing crazy people things like being a serial killer?
Example:
A. You are against cigarette smoking.
B. The Nazis were also against cigarette smoking[2].
C. Therefore you are a Nazi.
D. Optionally: I won't consider your argument unless you tell me why being a Nazi is ok. Why do you support anti-semitism?
The latest updated version of this is: What you believe is arbitrarily labeled a conspiracy theory. People that believe in conspiracy theories believe the earth is flat. Why do you believe the earth is flat?
[1] https://en.wikipedia.org/wiki/Association_fallacy#Guilt_by_a...
[2] https://www.goodreads.com/book/show/251213.The_Nazi_War_on_C...