To what degree are the Coen Bros films farcical?

What I enjoy about the Coen Bros is their ability to spin events which other filmmakers normally take seriously into satirical comedy. They're the type of directors to intentionally put historically incorrect (or otherwise non-sequitir) information in a film as a way to poke fun at fans who take the sort of thing.

To what extent do farce movies have the ability to do whatever they want and be immune to questioning? Typically, a questionable decision in a Coen Bros film is almost always defended with "it's a farce". At this point, can any completely arbitrary decision be passed as just a joke?

There's a difference between a "joke" and a "farce".

I think you'll have to be a lot more specific to get much of an explanation. Particularly since the tone of their films varies considerably. I wouldn't say No Country for Old Men is farce, or that one could explain anything in it away with that term, but films like Intolerable Cruelty, Burn After Reading, and Raising Arizona obviously are.

That said, pretty much all of them operate in a somewhat heightened reality.

I'd argue it just changes the balance of the kinds of criticisms you can levy against the movie.

If a movie is opting for realism, you can forgive muddled/conflicted tone because that's the way life is, while being more critical of parts of the movie that seem like impractical.

If a movie is opting for more fantasy, you can forgive improbabilities because they've established a bizarre setting, while being more critical of parts of the story that seem to be inconsistent with the thrust of the story.

I'd argue the problem is when a film tries to have it both ways, where if someone argues a film is erratic in its depictions and it's creator says "well life is inconsistent and the film reflects real life" they shouldn't also be allowed to say when someone argues the same film is fantastical and not representative of real life that "it's just a film therefore fantasy".

That said, I think the movies you're talking about are generally more fantastical, but those aren't immune to criticism. You can question those movies on whether or not the Coen brothers are able to levy this freedom from realism in ways that help the movie (if they don't they probably were better off being "realistic").

It's similar to the rampant problem with media dubbed "satire", where satirical films are generally describing a real world issue while using an absurd representation of the problem, so the film's defenders often feel like they slip back and forth on whether or not the film is "realistic". Where I'd argue in a satire the film either does a good or bad job on the cleanness of the metaphor and whether the metaphor was necessary (e.g. if a film is just making an obvious restatement that doesn't lead to any new insight into the issue, I'd say it's bad satire. If a film is bending the actual application of the problem in the real world so that it truly functions in a distinctly different way, to the point where any insight gained isn't actually translatable to the real world problem, I'd say it's bad satire. Idiocracy stands out as an example of both problems, IMO.)

And if the movies are just supposed to be funny and not carry any sort of metaphorical weight, then there should be extra scrutiny on how funny they are. Which is obviously pretty slippery. (But I don't think the Coen movies are pure comedies)