"‘Shared physical and genetic characteristics’ seems to put most people into several races at once by the time you’ve considered height, eye colour, acuteness of hearing, proneness to certain diseases, dexterity and so on indefinitely".
But you know what I mean though. Look at someone of Chinese origin, of Swedish origin or of Nigerian origin and you can clearly tell they are from different races. Look at Jews from different regions and you will see that they probably resemble other people from those regions more closely than they resemble Jews in other parts of the world.
". I would still say, without offence to Yonah I hope, that almost every idea of being Jewish that I know refers in some important degree to ancestry."
Not according to the state of Israel. If a person born to Jewish parents converts to a different faith he/she will not be considered a Jew in the eyes of the state. By contrast, if a Catholic or Hindu converts to Judaism he/she will have that 'privilege'.
And again the 'ancestry' in question is religious in nature - a Jew either practices the religion of Judaism or is descended from somone who did. They do not share a common (even if distant) geographical origin, as members of a certain race do.
Jews are not a race, no matter how elastic you make the term. Ethnicity, at most.