An odd example is the jew harp, which isn’t pejorative and also has no history or connection to Jewish people, culture, or history.
According to the page you linked to and the Oxford English Dictionary there may be a connection:
“More or less satisfactory reasons may be conjectured: e.g. that the instrument was actually made, sold, or imported to England by Jews, or purported to be so; or that it was attributed to them, as a good commercial name, suggesting the trumps and harps mentioned in the Bible.”
Of course the OED then discounts the other prevalent theory that the name is a corruption of “jaws” or “jeu” as baseless which leaves one other theory…
It has also been suggested that the name derives from the French “Jeu-trompe” meaning “toy-trumpet”
I know jewish people who refer to themselves as jews.
They’re probably anti-semites.
When I was growing up I never had that association either. Jews were a religious group in the Bible. I never heard of anyone living in the area referred to as being Jewish. I don’t a negative connotation about jew as a verb: he jewed him down–means he haggled him down. That’s a skill which I don’t have.
The important question is whether you continue to use the term now that you know that Jews are real people who usually object to the stereotype.
For reasonable people intent should count. You didn’t know the underlying meaning of the word, and I assume the woman I mentioned didn’t either. As a child I used the word ‘gypped’ without knowing its origin, it could have been spelled ‘jipped’ for all I knew. I don’t mean simply the intent in using the word though, once you know the etymology you have to own your usage of it. And none of us are perfect, we develop our vocabulary early in life and may unintentionally say something later when we should have known better. That’s what apologies are for.
Have you ever seen a German movie (guess what era) called The Eternal Jew? I can’t recommend watching it, but it would answer your question.
The common notion here – and thus, the common negative connotation – to the verb “jew” meaning “haggle”, is that Jews had a stereotyped reputation equivalent to what we would now call “greedy ruthless Wall Street Bankers”.
Are there anti-Jewish stereotypes? Sure, and many of them have been mentioned here.
But there are also loads of positive stereotypes about Jews. Heck, even virulent antisemites believe in many of the positive stereotypes!
People will say “I Jewed him down” when they got a price knocked down .
I was at flea market once and ran into one of daughter’s teachers who was a Black woman and she told her friends “She Jewed him down!” And I told her that I am Jewish and didn’t like that . I wanted to say to her " No you niggered him down!" and see how she liked it . But I didn’t want the teacher taking this out on my daughter at school. I have been call a Jew and the way it was said is was meant to be an insult. I personally feel the word Jew is only used as an insult. It’s the only way I heard non Jewish people use it.
I’ve asked several Jews about this and have received varied answers. I try hard to be mindful of language and its many effects on those to whom I am speaking. I was interested to learn that some do find a negative connotation. Others don’t.
As a non-Jew, however, I think Jews should own it. “Jewish” just seems so… non-committal. Don’t be Jew-“ish.” Be a Jew. 
That said, I make a point of being respectful of how people wish to be characterized and will abide by the majority opinion established in this thread. I don’t live in an area with lots of Jews so have few opportunities to learn their preferences. For that reason, I am interested in this discussion.
A lot of people don’t realize where “gyped” comes from either.
Whether the speaker intends offense or not is usually obvious - I most often hear it used (naturally and non-offensively) by people who are themselves Jewish.
The adjectival form is Jewish, whereas with blacks it’s the same word, black. We usually don’t refer to people as nouns of their group without some risk of insensitivity, if we are outside the group.
Anecdotes: In my mothers high school yearbook from 1954, in Northern Maine, there was a kid whose nickname under his picture was “Jew.” He was a hustler apparently and went into small business. My father happened to be a teacher there, having come up from New Jersey, a Jew. In all the years of looking at that yearbook when I dug it out no one mentioned it until a couple years ago when I saw it and it registered.
I just had a run in with someone on another website who went off on an anti hillary tirade and ended it with “And she would be the first Jewess president.” I saw it 35 pages into the thread and made a complaint. The person was irrational and ill. I sympathize but I couldn’t let it go. The upshot was that the moderator cited that the word “Jewess” is described as “offensive.”
Jews handled money because Christians would not. They were manipulated into this role because it was against church rules to lend money at interest. It was one profession they could take part in and not be barred from. It is especially hypocritical, and quite ironic to blame them for that.
Now that I think of it, if I’m asked about my own identity I’m much more likely to say “I’m Irish” than “I’m an Irishman”.
But I think this may be one of those areas in language where idioms are not always consistent. “I’m an Irishman” would strike me as stilted, but in my head I can imagine an American saying either “I’m American” or “I’m an American”. Neither sounds stilted and both strike me as the kind of thing I might here. (Am I wrong, American dopers?)
When it comes to religion, though, I’d probably say “I’m a Catholic” rather than “I’m Catholic”, and to my ear this sounds right for other religious positions (including atheism and agnosticism).
When it comes to gender, I’d say “I’m a man” rather than “I’m male”, and I’d expect a woman to do the same.
So, idioms here seem to be to be inconsistent. And, possibly, they may differ in different varieties of English. And, since Jew/Jewish can be both a religious and an ethnic/cultural identifier, the idioms might be particularly slippery with that one.
So, if you hear “he’s a Jew” and that strikes you as having negative connotations, it could be just because that’s not the idiom you would use or expect, but it might be quite natural to the speaker. The negative connotations could be all in your head, in other words.
Or perhaps not. Because, of course, there is a long history of of people speaking in a derogatory or pejorative way about Jews, and if we are now very sensitive to the possibility that partly reflects the fact that we need to be. Antisemitism hasn’t gone away.
I’d say, though, don’t worry so much about the noun/adjective thing and look at context. “Manny doesn’t eat pork - he’s a Jew” doesn’t have any more negative connotations than “Manny doesn’t eat pork - he’s Jewish” would have. In both cases, reference to Manny’s Judaism is entirely neutral.
The context here is there is an extensive history of “Jew” being used as an epithet, and Jews being subject to anti-semitism, genocide, being blamed for any number of wordly ills including everything from world and/or financial and/or media domination, to cosmopolitanism, to murdering christian children, to killing Christ. So yeah it’s a distinct situation.
I get that. But we might reasonably ask why “Jew” would be more freighted with negative connotations than “Jewish” would be.
And I think the answer may be, if we use “Jew” in a situation where the more usual idiom would call for “Jewish”, that serves to call particular attention to Judaism and, given that general context, we can’t avoid the suspicion that it’s intended to be pejorative.
But, the thing is, the idioms here are a bit slippery, and what sounds to the hearer like a deliberately emphatic use of “Jew” might not be intended in that way by the speaker.
Think of it this way. It’s okay to say “He’s one of us, he’s a Jew” and not okay to say “He’s one of them, he’s a Jew.” Compare a black person referring to another black person as “nigger” and a white person referring to a black person as “nigger.” Using “Jewish” as an adjective carries less emotional baggage. And using “Jew” as an adjective or verb is offensive.
The title was the reason the film was offensive? If only Gobbler had called it “The Eternal Jewish Person”, the Don would have been ok?