@Mooser: "So one might think, but the Jewish gene is inherited independently of any particular physiognomy. Either you got it, or you ain’t. "
You are correct to a degree. There isn't any such thing as a "Jewish gene". In terms of DNA, Jewish ancestry is inferred by the presence of genes found frequently in known ethnic Jewish ethnic populations.
None of these are exclusive to Jewish populations; they are just far more common among Jews than non-Jews. It's a matter of inference to best explanation based on empirical statistical analysis rather than a matter of a genetic Jewish 'watermark'.
For example, it's a common misconception that "only Jews get Tay Sachs" or "only Ashkenazi Jews have the defective BRCA genes associated with breast cancer"; this is absolutely NOT the case. It IS true however that these genes -though rare in all populations - are far more common amongst certain Jewish populations.
Ashkenazi, Sephardic, and Mizrahi Jews do indeed typically have a significant Levantine signature in their DNA consistent with a common origin in the Levant that roughly corresponds to the Biblical time frame.
However these groups also have tons of diaspora DNA, and scientists interpretations of just how much ancient Levantine DNA versus more recent diaspora DNA is present in the various Jewish ethnic populations varies wildly.
So there are "Jewish genes" in the sense that there are genes that occur much more frequently amongst Jewish populations than non-Jewish populations. However, if you are a full blooded Swede with a well documented family tree going back hundreds of years with no known ethnic Jewish ancestors, you may still be determined to be part Ashkenazi by one of these popularly marketed DNA tests if you carry one or more of these genes found most commonly amongst Jews.
Doesn't mean you necessarily have Jewish ancestry.
So it's complicated. There is undoubtedly a portion of the DNA of ethnic Jews that reflects common descent from an ethnic population. There are also genes that are found amongst Ashkenazi but rarely among Sephardic or Mizrahi, and genes found amongst Sephardic Jews rarely seen in Ashkenazi and Mizrahim etc.
My point is not that there is no such thing as 'Jewish genes' per se (in a sense there are), but all Jews have lots of 'non-Jewish diaspora DNA' as well.
Zionist/Israeli propagandists are actually very sensitive about ethnic divisions amongst Jews; its something they endeavor to sweep under the rug.
Historically, and especially after WW2, Jews and non-Jews alike generally eschewed the notion that Jews represented a race or ethnic group. Indeed the suggestion that Jews are an ethnic group with a distinct genetic signature was often regarded as anti-Semitic; the polite narrative was that Jewish identity is entirely a matter of religious belief, not ethnicity (like Presbyterians or Catholics etc).
In recent years however many prominent Jews have proudly called attention to the supposed remarkable genetic similarity amongst all Jews (Ashkenazi, Sephardic, or Mizrahi/'Oriental').
[Well, all except for Ethiopian Jews of course; they are quick to point out that Ethiopian Jews are descended from converts of course.]
As to the genetic similarity of Ashkenazi, Sephardic, and Mizrshi (or 'Oriental') Jews, if you know anything about inferring ethnic ancestry from DNA it's a bit like looking for images in clouds. What you see depends a lot on how you choose to interpret the data, and it is an area uniquely vulnerable to conscious or unconscious bias.
Pro Israeli media tend to report on findings that show the various Jewish communities as being closely related and ignore those that do not (i.e. they think it's "good for the Jews" - and for Israel).
I think a little common sense goes a long way here. The differences in phenotype between Ashkenazi and 'Oriental' Jews are far more dramatic than those between Europeans. There are Ashkenazi who look like Swedes and many are pale skinned and fair haired while there are 'Oriental' Jews that could pass for Pakistani. There is obviously a significant difference in the genetic heritage of these groups.