"Argle-bargle" is a term I've never encountered until I read Jennifer Senior's op-ed piece in The New York Times (September 23, 2020), called "The Ginsburg-Scalia Act Was Not a Farce." The article is about the friendship between Supreme Court justices Ruth Bader Ginsburg and Antonin Scalia, who were on opposite sides of the political spectrum. Ms. Senior described Justice Scalia as a "hero of the Federalist Society, defender of originalism, dreaded foe of progressive argle-bargle." [Italics mine.]
I looked up "argle-bargle" in my copy of the Canadian Oxford Dictionary, Second Edition (2004), suspecting the term might be a British import. The closest term in the dictionary is "argy-bargy," identified as of British origin and meaning "a dispute or wrangle."
Consulting one of my two battered copies of The Random House Dictionary of the English Language, I found the word "argufy," of no particular origin. It is defined as "to argue or wrangle, esp. over something insignificant." That's about as close to "argle-bargle" as I could get in an American dictionary.
"Argle-bargle" is one of those British expressions that have entered American speech, much like "gobsmacked," "shambolic," and "the full monty."
One clue to the origin of "argle-bargle" is Cockney rhyming slang. Lonely Planet's London guidebook (Lonely Planet Publications, 2012) says that Cockney rhyming slang "may have developed among London's costermongers (street traders) as a code to avoid police attention. This code replaced common nouns and verbs with rhyming phrases." For example, " 'going up the apples and pears' meant going up the stairs, the 'trouble and strife' was the wife, 'telling porky pies' was telling lies and 'would you Adam and Eve it?' was would you believe it?"
In the meantime, maybe I should send a copy of this blog post to Melissa Mohr, who writes the "In a Word" column for The Christian Science Monitor Weekly magazine. Ms. Mohr might be able to shed some light on "argle-bargle."