I understand that the Nazis made official exceptions for Karaite Jews although in practice this was not always followed and in fact they were not completely "exonerated" in Nazi "racial theory." My question is, did Nazis accept the Khazar theory of the origin of Ashkenazim and if so, did they see Sephardim as different (I think they did not). I do not expect consistency or logic from racists but I do wonder if the Khazar theory was used as a way to distinguish Jews or was the Khazar origin not widely known pre-WW2?
You have to think of Hitlers tyranny less as a ideology backed by evil people, but as evil people seeking backing by an ideology that they created and twisted whenever they saw fit.
Nazi's first and foremost ideology, as in any tyranny, was self-preservation and personal gain of wealth and power. Of the leader himself, but also of his countless sub-leaders in the hierarchy when it would not run contrary to the overall goals. They used antisemitism as it fit them and they allowed other priorities whenever necessary for their prime directive.
Good reasons to deviate from their ideology for personal gain was "allies" (in quotes because to them that meant people able to die in place of their own armies or as part of their armies) or helpers (as in forced labor) or sometimes, as cynical as that may sound, because it was too much of an effort to follow through on it.
In this case, Wikipedia gives you a few hints on what the Nazis might have seen in them:
Maybe potential "allies":
[In the previous war, they supported] a short-lived Crimean Russian liberal, anti-separatist and anti-Soviet government also supported by the German army.
Or at least friends of "allies" that they did not want to upset:
Discrimination against the Karaites is unacceptable, in consideration of their racial kinsmen [Berger was here referring to the Crimean Tatars]
So whatever paper was produced to legalize this, whoever thought about theological theory... he was just a tool for the leadership, to make it possible to work with the Crimean groups that hated the Soviets, too. Hitler did not care about religious theory. At all. Neither did his fanatical followers.