Title says it all. I’ve heard this cliche used in satire as long as I can remember, but was wondering what they were originally satirizing.
I believe they were satirizing Jewish-American culture, in which it is important to determine whether people you interact with are Jewish.
Or they were satirizing anti-Semitism in mainstream American culture, in which people were surprised to learn of the Jewish identity of individuals who didn’t seem to display any stereotypical Jewish traits.
This has been answered before, but I’ll go for it.
Two strangers are sitting next to each other on a ferry. One guys turns to the other and says:
“Hey, tell me you’re Jewish.”
The guy says “Excuse me? What? Why would I do that?”
“Oh come on,” says the first guy, “Just tell me that you are Jewish”
“No. Leave me alone”
“Just once! Come one!”
The second guy finally turns, exasperated and says “Okay, fine, whatever. I’m Jewish.”
The first guy says “Funny, you don’t look Jewish.”
I always thought it came from well-meaning but dim Gentiles, who were surprised to learn that people they knew were actually Jewish.
And I’ll share my own old joke:
A small, well-dressed man enters a Belfast pub late one night. Everyone glowers at him, and a huge bruiser soon gets up, walks over to him and asks threateningly, “Are you a Catholic or a Protestant?”
“Why, neither,” the new guy says, sipping his beer. “I’m Jewish.”
The bruiser is a bit taken aback at first, but then he snarls, “Are you a Catholic Jew or a Protestant Jew?”
It originated back with the Druidians.
Thanks, I should have searched.
Somehow I always imagined that it had a more sinister anti-Semitic origin possibly from WW2. Glad I was wrong.
I don’t buy that the origin of the phrase is in that joke. The joke itself implies to me that the phrase “Funny, you don’t look Jewish” is already familiar to the audience.
A story has Quentin Crisp addressing an Irish audience, and being asked if he was Catholic or Protestant. He said he was an atheist, and a woman in the audience asked, “Yes, but is it the God of the Catholics or the God of the Protestants in whom you don’t believe?”
This actually happened to my wife’s stepmother’s sister. It is not an urban myth, my wife was very close to her stepmother (a wonderful woman) and I know the sister, although hot well. She was a natural blond. Until the Anschluss, she was a nurse in Vienna. When she was dismissed from her job, she told her supervisor that she was leaving. When she explained that she was dismissed for being Jewish, he replied something like, “You, Jewish? What kind of Jews are they sending us?” Not quite “Funny, you don’t look Jewish”, but the latter had to be a known phrase to form the basis of a comedy routine.
Another phrase we are quite put off by is, “Some of my best friends are Jewish.”
Funny, they didn’t look Druish.
A woman on a train walked up to a man across the table. “Excuse me,” she said, “but are you Jewish?”
“No,” replied the man.
A few minutes later the woman returned. “Excuse me,” she said again, “are you sure you’re not Jewish?”
“I’m sure,” said the man.
But the woman was not convinced, and a few minutes later she approached him a third time. “Are you absolutely sure you’re not Jewish?” she asked?
“All right, all right,” the man said. “You win. I’m Jewish.”
“That’s funny,” said the woman." You don’t look Jewish."
I remember in one of the Who’s in Charge Here? series of joke books (cartoon captions put on actual news photos) from the early Sixties, JFK is talking to David Ben-Gurion, who has a puzzled expression and says, “That’s funny, you don’t look Jewish!”
I think the joke works just fine never having been familiar with the phrase. I mean, why in the world would someone bother another person so much about whether they are Jewish, almost insisting that they must be, only to have them say that they don’t look Jewish. I think it’s quite funny. And I’m no anti-semite.
Himmler asking a boy standing in line, about to be machine gunned?
From the other thread:
How about meta-joke? The punchline of the original joke could be anything. "Funny, you don’t look gay / Canadian / like a lawyer / doctor / cop / sick.
It’s a standard joke about ignorance and misconceptions which is probably as old as language. Of course the Jewish community would be familiar with “you don’t look Jewish” but the meta part is when two Jews do it. Plus Jews are funny. 
The other version with the woman pestering the guy until he says “fine, I’m Jewish” is meta I think because some people are so ignorant they’ll go out of their way to be ignorant even when it doesn’t make sense.
Just my guess.
The variation I always heard was, a man was walking through a deserted Belfast street late one night, when he felt a gun at his back. A voice asked him “What religion are you?”
The man was Catholic, but he was afraid to say so, knowing that if he said he was Catholic and the gunman was a Protestant, he’d be dead. But if he lied and said he was a Protestant, and the gunman was Catholic, he’d end up equally dead.
Thinking fast, he said, “Why… I’m Jewish.”
The gunman was silent for a moment, then chuckled, “Well now, I must be the luckiest Arab in Ireland.”
Maybe The Beatles started it.
In Yellow Submarine (the movie), the Chief Blue Meanie asks the Beatles: “Are you Bluish? You don’t look Bluish.”
The Beatles didn’t start anything, they must have stolen that joke from Chuck Berry.
I just did a Google Ngram on the phrase. There are scattered uses of it in books in the 1910’s:
It took off in the 1960’s though, and I remember uses of it on TV at that point. I suspect that up to that point it was still considered sufficiently offensive that it could only be used in a story to show that someone was either antisemitic or clueless. By the 1960’s, being Jewish was sufficiently mainstream that it was just funny that anyone would be that concerned about who was Jewish. The phrase has actually dropped off in use in the 2000’s, since the whole idea of someone thinking that much about whether someone else was Jewish is now considered slightly weird.