DG, I think I agree with some of what you're saying here, but I guess you didn't see my earlier post, which did attempt to answer your question. It's not correct to say Jews don't have a common genetic denominator. A recent study (I know I should provide a reference, but I don't have it offhand and don't have the time to look for it) looked at the Y chromosomes of Jewish men who identified themselves as Kohanim. These are the descendants of the high priests (considered to be descendants of Moses' brother Aaron, the first Kohen), who still have special privileges and obligations in the synagogue service. In Jewish tradition the status of Kohen is passed from father to son. In biology, a man's Y chromosome comes from his father, while his X chromosome comes from his mother. The study showed that nearly all of these men had a specific marker on their Y chromosome which was not seen in other Jews or in non-Jews. This suggests that all these men, who were selected on the basis of a belief that they were all descendants of Aaron, were in fact descended from a common male ancestor.   

This certainly does not prove that all Jews are genetically related; of course they are not. But as I mentioned above, a very large proportion of people who identify themselves as Jews base that identification on a common ancestral heritage. It's not exclusively based on choice. And for the Nazis, at least, their attacks on Jews were not based on a person's religious choice at all. Many Christians died in concentration camps because they had a Jewish parent or grandparent. (In fact, there was a persistent rumor that Adolf Hitler's father, Alois, was the illegitimate son of a Jewish man named Frankenberger. The rumor was persistently denied, but Frankenberger did make regular payments to Hitler's grandmother's family. For more on this, I'd recommend the fascinating book For Your Own Good: Hidden Cruelty in Child-Rearing and the Roots of Violence, by Swiss psychiatrist Alice Miller.)

For the record, I'm not a Kohen, despite my name. My grandfather's name was Kolchevni; he changed it when he came to America. The popular belief is that officials at Ellis Island changed people's names; in fact, most people changed their names to ones that they thought would sound more "American" and less "European".

Aloha,
Mark