Different claims have been made and have been easily disproven, however they remain.
Judaism relies on
matrilineal disent. Some may claim that the female lineage is the reason, however DNA shows mediterranean and southern Europe dissent. Methods of conversion are well established and probably more so at the time.
The Ashkenazic lineage was probably the beginning of the diaspora following destruction of the first Temple. The DNA shows a bottle neck occurred. This is why modern genetic testing is absolutely invaluable today. Too many horrific diseases. I disagree with some of the wiki reasons for the causes. The Ashkenazic were often forced separated as a community. There are both longevity genes, and many that will kill horrifically at a young age. Quite a strange dualism there. I joke "We" are a genetic dumpster fire.
Modern Ashkenazic Judaism suffers the same issues as say Catholicism. The modern state has become a false god. That is why I do not find offense with the term Jino. Then again, no one is perfect. What many "Jinos" don't understand and are in denial of, is the Lord ultimately will force them to remember it. By external forces or internally.
Do we have it right?
Yes and thank you for taking time to study it.