Now, I'm no biologist, but I have studied genetics in the past... and, correct me if I'm wrong, but there's less than one hundredth of one percent difference between any given 'race' of human beings. That's > .01 % . The point being that there is little, if not "none at all", biological basis for race. However disappointing it may be to hatemongers, we're all pretty much the same when it comes down to the protein chains that determine who we are.
That being said, I would thing that it would be difficult to develop a biological weapon to target just this small difference, if your only distinguishing feature is the genome of the victim. However, to transmit a disease culturally (as in your example, throughout Jewish people), may be feasible. However, the factor used to attack the victim would be culturally based, not racially based.