In reaction to this brouhaha, Brian Leiter elaborates upon some Nietzschean basics:

If the smear of Nietzsche as a “fascist” and “anti-semite” has no textual basis, it would be wrong to conclude that Nietzsche is some benign secular liberal: He is not. When the Danish critic Georg Brandes first introduced a wider European audience to Nietzsche’s ideas during public lectures in 1888, he concentrated on Nietzsche’s vitriolic campaign against morality and what Brandes dubbed (with Nietzsche’s subsequent approval) Nietzsche’s “aristocratic radicalism.” On this reading, Nietzsche was primarily concerned with questions of value and culture, and his philosophical standpoint was acknowledged to be a deeply illiberal one: What matters are great human beings, not the “herd.” The egalitarian premise of all contemporary moral and political theory — the premise, in one form or another, of the equal worth or dignity of each person — is simply absent in Nietzsche’s work.

The question about the basis of equality remains a live one in political philosophy: How can it be that we all have equal moral worth given that we are plainly not equal along almost any relevant dimension one can think of (intelligence, rationality, integrity, talents and so on)? Some contemporaries, like Jeremy Waldron, the current Chichele Professor of Social & Political Theory at Oxford, have argued that only with a belief in God can we find a basis for the moral equality of persons. Nietzsche would have agreed, which is why he thought the growing recognition that “God is dead” would be so momentous.

The implications of Nietzsche’s anti-egalitarianism remains a vexed interpretive question, though as I have argued elsewhere, the most plausible reading is that Nietzsche had no political philosophy, that his focus was increasingly esoteric, on transforming the consciousness of select individuals — his rightful readers — about the extent to which morality was really compatible with the flourishing of the kinds of genius he most admired, as exemplified by figures like Beethoven and Goethe. Whether or not that reading is correct, it is clear there is no evidence that Nietzsche supported a fascist state, and overwhelming evidence to the contrary. Nietzsche’s Zarathustra calls the “state… the coldest of all cold monsters… whatever it says it lies… Everything about it is false,” concluding that, “Only where the state ends, there begins the human being who is not superfluous.”