A quick note, modern anthropology as a discipline largely rejects the idea of 'race' (on fairly spurious grounds incidentally), so appealing to the 'anthropological' definition of race is fairly odd since there is no other discipline which is so vehemently and bitterly opposed to the concept.
Almost all serious genetic anthropologists agree with the reality of race. Only the extreme Social Scientist anthropologists deny the existence of race. I choose to disregard people who have a political agenda to deny obvious scientific facts, and falsify data (as Gould did with skulls) in order to justify it.
The evidence is just far, far too massive to deny from an evolutionary and genetic basis. You can list off profound and enduring biological differences between the races that clearly distinguish between populations in humanity.
As I noted in a previous post, you can identify:
Morphological differences - including the skeleton, musculature, skin, and organs.
Differences in gestation, twinning, and maturation.
Differences in intelligence.
Differences in reflexive responses.
Differences in disease suspectibility.
Differences in frequency of blood type.
Different Y-Dna and M-DNA lineages.
In fact, it would be a serious challenge against evolutionary theory if there were not human races. It would deny that environmental isolation produces manifest change in populations, undermining Darwinian selection entirely. In fact, it would require a miraculous occurence for human populations to not be dramatically different based on the thousands of years of development apart from one another.
We have reached the point where anyone with a few hundred bucks can have their blood tested and get an accurate test for the percentage of DNA they have from various regions of the world. This would be impossible if race was a social construct, as every population would be equally "baseline human" otherwise.
Is there crossover between the races? Sure, at the periphery. Have Anatolians seen more admixture between Indo-European, Semitic (both Caucasoid), and Turkic (Mongoloid) populations? Sure. Has Ireland experienced nearly as much? No. Has India experienced perhaps even more? (Maybe). But most of the exchanges of genes have been between distinct members of a broader race, than between distinct races. The one exception to this would actually be the Turkic element in the Middle East, which did contribute a significant Mongoloid admixture with the Caucasoid populations, although the ethnicity of most Anatolians share more in common with Southeast Europeans, and the Indo-Aryan/Dravidian admixture is more prominent in INdia.
It's really a popular concept that reflects the clustering of visible phenotypes, *reflecting* the relative genetic isolation of the individual's ancestors. In this sense it is biologically meaningful, but that is not because of anthropology. And this popular conception is not based on hidden genetic correlations, such that people who look identical are 'different races.'
Um, very rarely do people who look identical come from different races. And I am not saying that our political or social distinctions necessarily correlate with actual races (for instance, the US insistence that all Caucasoids are 'white', when the term 'white' means something different from Caucasoid, and certainly doesn't include Mesitzo populations). But yes, we can speak of anthropological races which make meaningful contributions to scientific discourse across the disciplines of archaeology, medicine, genetic mapping, et cetera.
As for Ashkenazim specifically, almost all genetic analysis shows them in-between Europeans and Middle Easterners (as stated in your own quotes above), and this is perfectly consistent with all the data indicating that is because they originated as Euro/ME hybrids. The narrowness of their genetics, and its being so prone to weird diseases, is best explained by the spectacular *bottlenecks* that Ashkenazim genetics have undergone, particularly the one where almost all Ashkenazim genetics descend from a group of around 300 people who lived a mere 700 (!) years ago. Amazing ... if you want to look for the 'specialness' of Ashkenazim genetics, these intense medieval genetic bottlenecks are where you'd start. For whatever reason, a relatively tiny group of medieval Ashkenazim spawned almost all of the modern Ashkenazim. Why that is so is a very interesting question indeed ... if you want to exalt the 'special' nature of Ashkenazim genetics, this is a much more plausible and easily demonstrated source rather than extolling ancient distinctiveness.
The half-distance works also along the lines of Israel as being broadly between Europe and Middle Eastern because the Jewish ethnogenesis occurred in Palestine, with populations of mixed ancestry present there. The Sea Peoples, the Philistines, Egyptians, Anatolian Indo-Europeans (Hittites), et cetera, were all present in ancient Palestine, and the Jews have long ties to this region.
Has there been some European admixture? Probably. But Ashkenazi have strongly ties with Sephardic and other Jews, much moreso than they have to any population in Europe. As noted: Eastern Europeans, where the Ashkenazi have lived for hundreds of years, share virtually no relation to Ashkenazi populations. At the very least, we're talking on the order of 1000 to nearly 2000 years of ethnic isolation. That is extremely enough to speak of a distinct people, an population isolate (or sub-race) of the Semitic, or if you prefer, a Semitic with Indo-European admixture family.
The OT was largely written prior to the conversion era. Judaism around 400 BC was a miniscule priestly cult, which presided over a set of mythical writings that exalted the priests and demanded absolute loyalty unto them and their temple. By 50 AD, however, there were Jews everywhere. What you see is a conflict between actual identification as "Jews," and popular conversions, and political use of forced conversion, and the priestly attempts to rail against foreigners. The Book of Ruth exemplifies this schizophrenia. In fact the OT would hardly have needed to rail against foreigner marriage *if it wasn't in fact such a widespread and prominent practice amongst the Jews*. These are priest bitching about the reality they face, and worried about losing control over their subjects.
It almost certainly was not so problematic for anyone but the ruling class. As we know from history, the most cosmopolitan of all peoples tend to be the rulers. Political alliances lead to marriages across cultures to solidify bonds of peace. The invectives against foreign wives were directed against kings and other men of high position who could get themselves foreign wives. I doubt the average farmer, carpenter, et cetera, was bagging him a foreign hottie. The Jews were not known for living in cosmopolitan cities or having an empire that encapsulated anything but the most closely related tribes of people.
"Jews everywhere" isn't entirely accurate. The Jews were clustered in Palestine and in enclaves in Anatolia. The Jews in Anatolia went there when Rome came in to make their fortune. It wasn't like you'd find Jews in Eboracum (York) at this time.
There were also, if I recall, a significant portion of Jews who remained in Babylon post-exile. This population was present in Babylon up till the Iraq wars of the last 20 years!
I would also not characterize Judaism as "miniscule" in 500 BC. Archaeological evidence does suggest a Jewish presence in the Holy Land. But it would be wrong to think of them as Romans or Persians in their extent of holdings, because that'd be ridiculous. The Bible exaggerates the importance of Judaism compared to other populations in the world, but it doesn't lie when it says "Jews were here in 500 BC". Whether or not it lies about where Jews come from beyond that - stories about Abraham and Moses - I can't tell you.
