I'm a bit confused re the ethnicity that constitutes Jewishness.
What follows is what I think I know. I'll keep it brief(ish) but I've got a real interest in the subject so would appreciate anyone who knows more about it than me, telling me if this is all bollocks.
OK, the root of Judaism is Hebraic and before Rome sacked Jerusalem, most likely the vast majority of people considered to be Jews were Hebrews. But since the Jews were expelled from Israel, and dispersed among Europe, you had two main groupings, the western and the eastern. The western became the Sephardic, and those in the east spent hundreds of years mixing with Turkic, Slavic, and Eurasian peoples, gradually becoming more and more detached from the Hebrew root of Judaism. Not just genetically mixing with other ethnicities, but forgetting the old culture, language, dietary laws, etc.
In Muslim Spain, the Sephardic Jews had more freedom to move around the core centres of Judaism in the Middle East - which they wouldn't have been able to do easily if living under Catholic rule which forced Jews to convert. So the western Jews retained the Hebraic root more prominently.
Then much later on, when the Latinised Jews moved from where they had been settling in Germany further to the east, to the slavic territory (the migration fuelled, at least in part - and inevitably - by anti-Semitic hatred), then they gradually mixed with (and taught) the Jews they met in the east, trying to get them back in touch with their Hebrew roots. The mixing of languages, mainly German and Hebrew but with Slavic influences etc, gradually formed the language Yiddish.
Over all that time you've got Gentiles converting to Judaism and mixing into the pot too.
So it must be conceivable that a lot of Jews aren't that strongly Hebraic at all - as there are so many possibilities in terms of lineage for them. They could come from a Greek line that converted to the religion 1500 years ago or whatever.
If you bothered to read that, cheers.