"So, by your logic, Jews should follow nazi ideology on who should be a Jew? "
And Israel has, as the Law of Return was amended in the 70's. In a way, this is an 'unwritten' amendment to the Talmud.
Look, I think the talmud is an interesting work, but it is, correct me if I am wrong, codified commentaries on the Law. That's just some old rabbi's opinion on who is a Jew.
Now, say I'm wrong for the sake of argument. G-d orally told moses you're only Jewish if your mother is Jewish, MOses for some reason didn't write it down explicitly, then thousands of years later it gets written down in the Talmud. What about being part of the tribes of Israel, as the tribe is paternally determined. Would someone with a Jewish father be considered of the tribe then albeit the mother not being Jewish? Doesn't that create some kind of problem?