If these "Jewish Diaspora" numbers are real, they must include "Sephardic" genomes as well. I just checked all my Italian 23andme shares. Quite a few show .1%, but that's noise level. It's generally proposed that it has to reach at least .2 to be likely real.
Another interesting thing I discovered is that out of all my Italian shares, including Sicilians, Calabrians and Neapolitans mainly, with some Abruzzese, only one group of Calabrians from one particular area show elevated Ashkenazi, from .4 to 2%. Calabrians from another part of the province showed none.
The area with 1-2% happens to be the area chosen by academics for an autosomal analysis of Calabria. Going by what I see from 23andme, this area may not necessarily be representative of all Calabrians. This is why, in a country like Italy, it's important to get lots of samples from lots of different areas. There are too many little isolated areas with a lot of inbreeding which may skew results by a couple of percents.
Oh, also interestingly, the "Near Eastern" + "North African" in that area is quite low by 23andme parameters, with the "Near Eastern" Caucasus like numbers from 1.5% to 10% and the "North African" (Palestinian, Arabian, North Africa) numbers from .6 to 1.5%. The person with the lowest "Near Eastern" and "North African" numbers is the one who scores 2% Ashkenazi.
This also shows, once again, that a lot of these numbers for southern Italians supposedly from 23andme are just a fabrication or have been cherry picked.