Christianism is a beta religion, more specifically ISTj-ENFj. Jewish culture is ISTj (strict adherence to norms and traditions, obedience to god [hierarchy], patriarchal family structure, etc) and the reform of Jesus (if he ever existed) seems ENFj (give the totalitarian jewish culture a more benign face).
The fact Nietzsche wrote the "Antichrist" shows that he hated beta values, which indicates delta as first option and gamma and alpha as second option.
He admired the philosophy of Siddartha ("Budda"), which is heavily based on Ni. That means alpha is the least likely option.
The way he wrote his books gives me the feeling that he was an extrovert, because extroverts, as a general rule, rarely write extensive books. Extroverts find it difficult to think first and write later, so they write more concisely. Just like the "little book" of Einstein.
So ESFp, ENTj, ENFp or ESTj.
Being a philosopher intuitive seems far more likely than sensing.
Between ENFp and ENTj, I pick up ENFp. The Ubermensch demonstrates that his visions were aristocratic and not democratic, so delta and not gamma.
The often-repeated tale states that Nietzsche witnessed the whipping of a horse at the other end of the Piazza Carlo Alberto, ran to the horse, threw his arms up around the horse’s neck to protect it, and collapsed to the ground. (The first dream-sequence from
Dostoyevsky's Crime and Punishment has just such a scene in which Raskolnikov witnesses the whipping of a horse around the eyes (Part 1, Chapter 5).[9] Incidentally, Nietzsche called Dostoyevsky "[t]he only psychologist from whom I have anything to learn." (Twilight of the Idols, Friedrich Nietzsche, 1889, §45).)