Je n’avais jamais entendu le mot (je ne suis pas Belge) mais il me fait tout de suite penser à carabinade.

Une carabinade, ou blague de carabin, est une farce, une plaisanterie, en général de mauvais goût ou paillarde, qui tire son nom des carabins, nom familier donné aux étudiants en médecine.

Le suffixe -ouille donne « une note plaisante, populaire, argotique, diminutive voire affectueuse à un mot ». La connotation « affectueuse » diminue la portée du mot, une carabistouille serait un peu moins de mauvais goût qu’une blague de carabin.

Origine de carabin :
Carabin est apparu au XVI^e siècle pour désigner un soldat de cavalerie légère (origine incertaine, peut-être du moyen-français (e)scarabin « ensevelisseur de pestiférés », l’expression carabin de Saint-Côme s’appliquant à un chirurgien. L’évolution sémantique s’expliquerait par la réputation des soldats dits carabins de faire rapidement mourir leurs patients. Le mot s’est diffusé au sens « d’étudiants en médecine » (source : Dictionnaire historique de la langue française, sld A.Rey).

If nothing else, the following “answer” as a whole and most of its individual parts might serve as prime examples of “des carabistrouilles”:

Although the accepted answer (resemblance to/possible derivative of carabinade) is very logical and extremely likely to be correct, there is a possible significance in the last two syllables of the cool word at issue (thanks for sharing it) that struck me as worthy of mention.

According to TLFi/CNRTL, the word “bistouille” (which is letter-for-letter the last two syllables of your word) can mean either cheap brandy (=“Mauvaise eau de vie”) or coffee laced with brandy (or depending, I suppose, on how you care to see and/or taste things, “Brandy laced with coffee”) (=“Café additionné d’eau de vie”).

The “coffee/brandy laced with brandy/coffee” sense is specifically listed as a regionalism from the French Department (le Nord/59) having the longest common border with Belgium, and the entry’s etymology/history section seems to imply that even the “cheap brandy” sense originated in the “59.”

All of this to say primarily that there appears to be a Belgian (or at least a northern French) connection between the last two syllables of your word and the notion of cheap and/or laced brandy.

Admittedly, however, this connection explains neither the first two syllables (“cara”) nor how or why “cara” + “bistrouille” could possibly mean “une histoire absurde ou une sottise monumentale.”

Alas, the only way for me to even try to explain those last crucial two issues requires pure (read: “far-fetched”) speculation on my part, as follows:

In English, the idea of someone talking foolishly/spouting hogwash is sometimes related to/blamed on the affects of too much alcohol, which idea can be expressed as:

That’s just the [rotgut] brandy talking.

English even has a word (i.e., “moonshine,”) that directly connects, in that single word, the notions of both “illegal [homemade] whiskey” (granted, not necessarily of poor quality) and that of foolish talk or ‘”nonsense.”

Unfortunately (that is, for the purposes of this “answer”), this is a French forum, which makes the connection in English mentioned above irrelevant here, and what’s even more unfortunate is that finding an irrelevant English connection has failed (this time, for it often does work) to lead me to a relevant French connection between:

“bistouille” (or any form of alcohol) and “une histoire absurde ou
une sottise monumentale,” …

… except for the rather weak (albeit literal) one of:

C’est le vin/l’alcool qui parle.

(And it wouldn’t help my argument at all to mention [except here for the sake of honesty] that both French and English, via Latin, have the notion of there being “truth in wine” [in vino veritas], which clearly contradicts, not only the “alcohol=nonsense” connection that I’m trying desperately to make/find in French, but also the very one in English that I’m claiming does exist and relying on herein.)

Anyway, even if an idiomatic French connection between over imbibing and sometimes fabricating absurd/embellished stories could be made or found, that would still require the use of some pure “carabistouilles” (like the following three examples) to try to explain what the “cara” means or where it might come from (but having made it this far, here goes nothing):

?“cara[fon de]bistrouille//cara[fe de]bistrouille”? =
?“[That’s] a pitcher’s worth/crock of moonshine/bulls^^t.” ?

?“car[a^]bistrouille”? (where “car”=“because/due to” [^but it
wouldn’t account for the second “a”]) = ?“[That’s] due to the
moonshine//[That’s] the moonshine talking.” ?

?”carabistrouille“? (where “cara” is a mispronunciation of “gare
à”/”watch out for”) = ?”[Watch out for] the affects of moonshine.”?