Christian Identity is just White Nationalists/Nazis desperately wanting to have their cake and eat it too.
On one hand, on some level they acknowledge Christianity as the truth. On the other hand, their pride cannot suffer the concept of Christianity being strongly rooted in a Hebrew/Judaic background, and that they would have to humble themselves by acknowledging being Gentiles adopted by the Mercy and Grace of God. Not to mention it clashes and creates a paradox with their White Nationalist worldview that they wish to force Christianity to conform to.
Thus, they resolve this cognitive dissonance by making up this elaborate fan-fiction about Gentile Europeans being the REAL Jews all along (in spite of the fact that the European Romans and other non Judaic peoples, like the various other non-Hebrew tribes of the Middle East, are singled out as Gentiles.)