Robert Solomon and Kathleen Higgins try really, really hard to differentiate Nietzsche from his sister, but they ultimately fail for the following reasons.
Nietzsche's emphasis:
1. The Roman Catholic church did a terrible job with morals, and morals are God, so God is dead. He never existed.
2. You should make your own morals, that correspond to life, unlike what the church did.
3. Making your own morals makes you the ubermensch, who is superior to the untermensch, who purvey false morals that do not correspond with life.
4. The world is meaningless, but you can create your own meaning (positive nihilism)through choosing life and being an ubermench.
Nietzsche's sister's emphasis:
1. The Roman Catholic church did a terrible job with morals, and morals are God, so God is dead. He never existed.
2. You should make your own morals, that correspond to life, unlike what the church did.
3. Making your own morals make you the ubermensch, who is superior to the untermensch, who purvey false morals that do not correspond with life.
4. The world is meaningless, but you can create your own meaning (positive nihilism) through choosing life and being an ubermench.
5. Create your own meaning by exterminating the Jews.
Academia says that obviously, because of point 5 not being common to both siblings, Nietzsche never had the first four.
But this is a blatant logical fallacy. Nietzsche wrote his books far in advance of his sister's work. I do not see much evidence that she rewrote his works already in print, rather than merely patched together his notes, and apply anti-Semitism, of which I have not seen so far. She never radically rewrote anything; she applied everything. She applied Nietzsche's system to her own morals. There is nothing in Nietzsche's system that opposes her doing this, because there is nothing to say that she did wrongly, except force. When you take God out of the equation, man is no longer viewed as a bearer of God's image, so life can be redefined. All races outside of the ubermensch's can be defined out of life. There is no transcendent ethical compass without God, and if you reject Him, you ultimately reject life. If there is nothing beyond "life" then what is, is right. Might makes right, and justice is whoever is strongest.
Positive nihilism and racism are not mutually exclusive. Germany's positive nihilism took the *shape* of racism. This is not to say that all nihilism is inherently racist, or that racism is inherently nihilistic. Germany under control of the nationalist socialist workers party largely rejected moral and religious principles, and replaced them with racially-based tribalistic morals.
How do we know that NS did not completely overhaul all of N's books, leaving an entirely different philosophy? We speak of N speaking well of Jesus in Z, but what if that was written by NS? Why did N's 40 friends which he sent copies not decry NS's rewriting, if it were so changed from N's vision? Why did his friends say nothing, if his vision was so obviously mangled? Is Z corrupted, or just edited? It does not matter who authored what if they are both positive nihilists.