So the Nazis weren't really racist? The death camps were more of an anti-religion kind of thing?
Actually, sort of, to an extent. From Wikipedia (which references other sources):
Anyone with three or four Jewish grandparents was to be exterminated without exception. In other genocides, people were able to escape death by converting to another religion or in some other way assimilating. This option was not available to the Jews of occupied Europe, unless their grandparents had converted before 18 January 1871 [the day the German Empire was proclaimed]. All persons of enough recent Jewish ancestry to be considered a Jew were to be exterminated in the German occupied territories. The Holocaust
This is clearly not a purely religious classification (as converting away from Judaism is not relevant from 18 January 1871 onwards). However it doesn't seem to be a purely racial classification either, on the face of it, since the lineage is traced back to people who were adherents of Judaism on the 18 January 1871 (unless I've read it wrong).
That said, I guess that would be adherents of Judaism according to some official record, and people may be unlikely to officially denounce a religion their parents believe, even if they don't believe it themselves, so in practice the point may be somewhat moot.