What you admit here is that being born to a Jewish mother makes one a 'Jew'. So there is a problem to identify this. It cannot be genetic or phenotypical. In fact, the phenotype of the father does not matter at all. A black guy theoretically could have children with a Jewish girl, and the children would be Jewish… So there is no genetic or phenotypical distinction as a Jewish identity. There can be a common phenotype, yes, but it does not necessarily correlate to the "Jewish identity".