Let me begin by saying that while this is fun for me to speculate about, I consider it pretty unlikely. But it is true that my matrilineal great-grandmother was named Kurkiewicz and came to America from Poland around 1900. Would it have been likely (or even possible) that a Jew emigrating to America at that time would go “into the closet,” so to speak, given the pogroms that were going on in Poland at around that time? Were any Jews at that time and place sufficiently secular or impious that they’d renounce their faith to avoid anti-Semitic hassles?
Secular Jewishness was indeed fairly common at that time and place.
Not relevant to you personally, but I’ve heard that many Jewish girls, particularly infants, were taken in by gentiles during and before WW2. Boys, having been circumcised, were less easy to disguise and were less lucky.
It is certainly possible.
Most immigrants around the turn of the century didn’t hide their Jewishness. That happened later, after the Nazi persecutions began. So, I’d say it’s possible but unlikely.
But if your only evidence that she was Jewish is the family name, that makes it even less likely. Many names which “sound Jewish” to modern Americans are simply “East European”, which we’ve stereotypically come to associate with Jews, but it’s not really accurate.
There are the “hidden Jews of New Mexico” and there is an interesting history of crypto-Jews in that region. They were descendents of Spanish Jews forced to convert during the inquisition. They were publicly devout Catholic converts, but secretly stayed true to their faith and practiced at home. Once they fled t the New World, they continued the hidden worship practices.
I read a neat article in a magazine a bunch of years ago while I was traveling in the southwest in which the author describes being raised Catholic then being told by his father that he was Jewish when he was turning thirteen. They made a really cool radio series in the late 1980s interviewing the descendants who still practice “hidden” Judaism.
Does that count as a smidge of European history?
At the turn of the century, Poland was about 14% Jewish. While that is a lot, it was still 86% Christian and almost exclusively Catholic. So it’s possible, but the immigration process would probably make the immigrant less likely to hide their ethnic identity anyway.
It may also help your investigation if you knew if that was your great-grandmother’s original name, or had it voluntarily or involuntarily changed upon arrival in America.
If she was baptized Catholic and you know which town in Poland (or more accurately in 1900: Eastern Germany & Western Russia) she came from, you can probably find her baptismal records if you do enough searching through the Mormon archives. Of course, that won’t answer the question of whether or not her family was secretly practicing Judaism at home while putting on a Catholic front in public.
C K Dexter Haven:
I can’t speak to “most” as I don’t know percentages, but it wasn’t Nazi anti-semitism that made many Jewish immigrants hide their roots, it was American anti-semitism. Jews who needed jobs would find themselves shut out in similar fashion to Negroes and Irishmen.
In line with the above, my understanding is that Poland today ( sadly now home to very few self-reporting Jews ) shows a higher incidence relative to other European populations of stereotypical “Jewish” genetic markers. Such that it appears likely that a fair number of Jews assimilated over the centuries to the point of becoming Poles. So even if your family wasn’t self-consciously Jewish when they immigrated, they still may have been so anciently.
Still not super-likely, but possible. You’d need to do some genetic testing to tease that out if you were curious.
Actually, most east European Jews came from ethnic German stock, and German-language names (or, in the case of Yiddish, German-dialect names). Many Jews moved to eastern Europe in the Middle Ages, as the rulers were actually quite open-minded.
However, Ithink a key question here is "what do you mean by “Jewish”. If you take the tradiutional Jewish answer, that anyone born to Jewish mother is Jewish, then there might be very few non-Jewish people in the world. Jews emigrated, even early in history, as far away as China, and retained their identity for some time. Or do you mean a substantial Jewish “heritage”?
Kurkiewicz isn’t a particularly Jewish name, though. It means “Son of the chicken”, and is fairly common in Poland, and a lot of Poles who weren’t Jews came to this country around 1900 too.
“Son of the Chicken”…? Man, I’d be changing that to “Slayer of Bears Blindfolded While Standing on One Foot” and it would have nothing to do with hiding any Jewhood. 
ETA: Me being blindolfed, not the bears. That wouldn’t be fair.
Could you have Jewish ancestry and not know it? Yes.
But if you wanted to convert to Judaism (at least to Conservative Judaism like I did), you wouldn’t be required or encouraged to scour through your ancestry to make sure your mother wasn’t secretly Jewish. A rabbi would probably take your word for it, and your conversion process would be pretty much like anybody else’s.
I wonder what they would do if a descendant of a crypto-Jewish group like the ones in New Mexico wanted to join a more mainstream synagogue and live as openly Jewish. (I suspect it would vary among rabbis)
Yes. A branch of my family tree (probably) did exactly this. I didn’t find out until my late 20s, and my father found out the same time I did.
Can you inherit ‘Jew’ in your genes? I really don’t ken the OP’s question, what has your ancestry got to do with personal choice of belief?
Or is Judaism an ‘Old Boys Club’, do you have to know someone (i.e be related to someone) to get in?
Cecil has spoken on this: Can you be an atheist and still be Jewish? - The Straight Dope
Nice one, cheers for linking :).
There are many layers to the OP’s general question. Given the longstanding presence of Jews in Europe, I’d say that most Europeans probably have greater than zero Jewish ancestors if you take the long view. Whether that’s traceable through genealogies and / or DNA testing is another matter, and whether it’s the direct maternal line (what “counts” in Judaism) is another matter still.
As for a specific individual immigrant around the turn of the 20th century, I’d say unlikely but not impossible (see stuthehistoryguy’s post). Even if they disguised Jewishness at immigration, there would be no real reason to hide that for the rest of their natural lives unless that was a change they wanted to make anyway for whatever reason.
stuthehistoryguy, how did you find out? What is your evidence?