@Witch Hunter Siegfried this admixture is what I am arguing makes them a different people. If a white person's descendants keep racemixing with asians, his descendants will be asian (a rather extreme example, but it still holds water).
After Emperor Hadrian nearly exterminated the jews, those few who survived who wanted to maintain this identity had to run outside of the empire. (let's not forget that within the same century the diaspora revolt and the punitive massacres after it also occured)
Those who remained in the empire had to get new identities and gradually assimilate into the more urban and "diverse" areas (by ancient standards) of the empire.
What I am arguing is that kikes ( whether mizrahi, sephardi or ashkenazi) do not have more "ancient jewish" admixture than Italians or Greeks (who had sizeable jewish diasporas). And that this is not enough for neither of these people to be called "jews".
(in case of kikes, they're more like a cult whose members belong to the three predominant ethnicities).
By taking the kikes' word for it when they tell you they have a 3500+ year old history, you are just legitimizing their claim to being a resilient people who do not fade with time.