This has been bugging me for months now. Not namely how to explain whether they are white or not, but whether they are Jews or not (or the fundamental other). The Whiteness can be determined after this.
Who is even a Jew?
-If 1 drop somewhere in bloodline makes one a Jew (ala pastor Anderson hypothesis), then there are many more Jews than we think, and some of them were invariably considered and acted like non-Jews. So, it isn't one drop.
-If Jewish mother makes one a Jew, then what about all the recognized Jews that acted in interest of Jewry that didn't inherit it from mother's side? Are converts also not performing in the interest of Jewry making a "better" Jew than Shlomo down the street? So it isn't just the inheritance on mother's side.
-Is it the religion? Obviously not, since there is a huge amount of (what we recognize as) Jews being irreligious, some historically even converted to Christianity then acting in the interest of Jewry. So it is not a religion.
-Is it significant amount of genes? What if I told you that based on your 2% Ashkenazi genes you will be persecuted? Would you not act in the interest of self-preservation or in the interest of Jewry? So, it isn't necessarily a significant amount of blood either.
-Considering above, what if I tricked you into believing that your tests results returned 20% when they had merely 2%? Or what if I tricked you that they had 2%, when you were in fact 0%? Would you not in either case act in the interest of Jewry if you were convinced that your life is in danger by virtue of being recognized as Jew, similarly as those rare converts?
So after all of this, it appears that there is virtually no criteria for being a Jew. But it is only so at first glance and there is indeed a common theme we can extract from this. Someone said in one of the talks (I think it was Spencer) that those carriers white genes scattered through the middle east are not necessarily what we would consider European Whites simply by virtue of genetics (therefore one of us). There is some truth to this, as many of them would probably see us as fundamentally other.
It is my conclusion that a Jew is the one that has potential for identifying with Jewry (and as a Jew), and by identifying with Jewry (and as a Jew) he sees Whites as the other because historically whites and Jews were always at odds (there might be a common appearance, but there is no common cause - which was in fact always in conflict). The feeling otherness or historical (and current) persecution fortifies their view that they are separate. Otherwise, many of Ashkenazis with significant white intake would pass as whites or perhaps even act as whites were they not familiar with their ethos.
So how does this answer OP's question? "Whites" are a group that does not by necessity make it's subgroups at odds with each other. While there may be wars in historical sense, there is no eternal struggle between English and Croats, Germans and Swedes, Russians and French etc. Jew, on the other hand, is in eternal war with all of those subgroups, and not one of them is it's friend. Therefore, even if some of them appear white, they fundamentally have nothing in common outside of that.
I'd like to hear your thoughts on this line of reasoning.