What you call "Jewish DNA" evolved for millions of years before Abraham, mixing freely with other Mediterranean and Middle East people for most of this time.
I'm not against the use of taxa below species level for humans; Its use is widespread on life sciences, but we need to apply it wisely. Race was a poorly defined biological term kidnapped to justify doing evil things against other people. The term may be a lost cause at this moment.
If we take a look to a Wolof from Senegal near an Aboriginal from Camberra we can always say who is who. If we take a look to somebody from Israel and somebody from Palestine, we can't. At the naked eye, both are indistinguishable. At a physiological level, both breath air and work exactly in the same way. Genetic differences between both are smaller than current genetic variability among Jewish.
If Jewish are some kind of taxon below species level, we would have to include Palestinians (and a lot of other Middle East people) on that taxon. This is how Taxonomy works.
If the reason is because they were a closed group for some time; applying the same reasoning, the European monarchies should be also a race. Is also a reproductive closed group, showing high frequencies of some rare diseases and even developed an unique look as consequence (See a portrait of Charles II from Spain).
Anthropology books should talk about Africans, Caucasians, Asians, Jewish... and Kings.
Why stop here? Should Mormons be also their own human race? Are Amish a race? Are rednecks a new race of humans?
The obvious answer is not. Maybe in 65000 years, but not now.
That would introduce a lot of noise in Anthropology, just for fulfilling a wish of "but I feel special", and should be avoided. We all feel special.