This is just the same (lazy) warmed-over guilt by association from the Nazis' vulgar interpretations of his works

Not really that vulgar when you look at what Nietszche thought about Jews:

There is only nobility of birth, only nobility of blood. When one speaks of “aristocrats of the spirit,” reasons are usually not lacking for concealing something. As is well known, it is a favorite term among ambitious Jews. For spirit alone does not make noble. Rather, there must be something to ennoble the spirit. What then is required? Blood.

What follows, then? That one had better put on gloves before reading the New Testament. The presence of so much filth makes it very advisable. One would as little choose early Christians for companions as Polish Jews: not that one need seek out an objection to them — neither has a pleasant smell.

Do I still have to add that in the entire New Testament there is only one solitary figure one is obliged to respect? Pilate, the Roman governor. To take a Jewish affair seriously — he cannot persuade himself to do that. One Jew more or less — what does it matter ?