My first thought when I saw your question was of the dubious record of the ancient Greek poet Sappho's husband.

There's an excellent response by u/Iphikrates in this thread that gives a run-down.

Basically, The Suda, a Byzantine encyclopedia, records the name of Sappho's husband as Kerkylas of Andros. Various later historians figured out that the guy's supposed name means something like "Dick Allcock from the Isle of Man".

Per u/Iphikrates in the thread, modern historians have theorized that the name started as a joke in a now-lost comedy play and by time it reached the author of The Suda, it was misinterpreted as a real historical detail.

How about the opposite: three years ago, resident moderator /u/J-Force argued that Machiavelli's "The Prince" has been reinterpreted as a Straussian satire, but AskHistorian threads on the matter show it to be more of an urban myth. There's a number of threads on this topic in the last ten years and all pretty much agree that this statecraft handbook was written honestly, despite the popular notion of its satire.

I belatedly thought of another example of interest, which unlike the Sappho one, is not funny. And which seems relevant to note, because if you search "Rothschild", you can see how there's been a lot of questions about this myth on the sub-reddit.

Specifically, there's a widely reported "fact" that's made its way into various biographies and works of non-fiction that the Rothschild family made its fortune by some sort of insider trading chichanery following the Battle of Waterloo. Including in some versions by tricking people in England into believing they had lost.

There's an authoratative discussion by u/mikedash in this older thread.

I think it fits what the OP is asking about, because the story started as an anti-Semitic calumny in a pamphlet, but over time, got repeated by non-polemical writers who in turn were cited in otherwise reputable books. For extra points, as discussed by u/mikedash, one of the works which helped disseminate the legend was a forgery called the Gallatin Diary.

What I find interesting about the myth is that once you know of the original context, you can see the parallels to other anti-Semitic conspiracy theories, like the one about Jewish World Trade Center employees having prior knowledge of the 9/11 terrorist attack.

But outside of that context, the implied accusation of dual loyalty and treason is less obvious. And it seems like just a cool origin story.