Who is a Jew, indeed

The young French man recently tortured and killed on account of being Jewish would not, had he lived, have been able to get married in Israel:

Richard Prasquier, the president of the Jewish umbrella organization CRIF, said [the victim] Roumi had a non-Jewish mother and his father “is not connected to the Jewish community.”

Is this discrepancy something we should praise, as in, Jews are not letting anti-Semites decide who counts? Or is there something altogether screwed up about using a religious definition to define a population that neither defines itself nor is defined by others as exclusively a religion?