It would be a long task to juxtapose Machiavelli's and Nietzsche's views about Christianity, but there is solid material in Machiavelli which is explicitly ant-Christian and which, on reading, matches a wide segment of Nietzsche's critique of Christianity.
Did Nietzsche read Machiavelli ?
Von Vacano identifies references made by Nietzsche
to Machiavelli (in e.g., Human,All too HumanH V:224; Beyond Good and Evil 28; Twilight of the Idols, "Ancients" 2; Will to Power, 201, 304, 776; and a passage
from Nachlass 1888), counting references to Machiavelli in "eight passages of his [Nietzsche's]
published work and in nineteen of his published notes" (76n21, 105). (Rebecca Bamford, 'The Art of Power: Machiavelli, Nietzsche, and the Making of Aesthetic', Journal of Nietzsche Studies, No. 38 (FALL 2009), pp. 95-99 : 96;
Diego von Vacano. The Art of Power: Machiavelli, Nietzsche, and the Making of Aesthetic
Political Theory. Lanham, Md.: Lexington Books, 2007. xi + 215 pp. ISBN-13: 978-0-7391-1088-1.)
Reading is one thing; influence another but given the similarities of viewpoint outlined below, influence appears probable.
Much evidence exists in the Discourses to bear out Hulliung's view that
Machiavelli's "anticlericalism ... marks only the first layer of his condemnation of Christianity. . . . Christian values per se are attacked as
corrupt and contrasted with the virtuous values enshrined by pagan
religion." Indeed, Machiavelli's preface to the first book characterizes
his intent as one of imitation of the pagan world. He states there that
although the methods of antiquity hold authority in certain disciplines,
in matters of the military and political arts the moderns do not recur to
the examples of the ancients. In ascertaining the cause for this neglect of
ancient examples, he says cautiously that he believes
that
this arises not so much from the weakness that the present
religion has conducted the world or from that evil done to many
Christian provinces and cities by an ambitious idleness [uno
ambizioso ozio], as from not having a true understanding of histories, reading them, but tasting neither the sense nor the flavor
that they have in them.
Although he hesitates to state directly that Christianity is responsible for
the failure to appreciate ancient history, Machiavelli forthrightly associates Christianity with the world's weakness. This weakness seems evident
in the fact that people judge that the imitation of the ancients "is not
only difficult but impossible, as if the heaven, the sun, the elements, and
human beings, had changed their motion, order, and power from what
they were formerly."
...
It appears that, in Machiavelli's view, Roman history can instruct
moderns even in matters of religion, for early in his section on religion,
I 11-15, he asserts that a return to the methods of the Romans is possible.
He proclaims: "Let no one be discouraged about being able to achieve
that which was done by others, because human beings, as was said in our
preface, are born, live, and die always in the same order" (I 11). By
placing this emphatic statement in the context of his discussion of the
pagan religion, he appears to offer his examination of the former religion
with a view toward the possibility of achieving "that which was done by
others."
Machiavelli makes the need for such imitation in matters of religion
prominent in II 2, when he treats the political effects of Christianity. He
ponders why modern states do not demonstrate the same degree of determination in the pursuit of their liberty as did the ancient Italian republics
that stalwartly defended themselves against the Roman threat. He
answers his question by referring to the difference between the education
of the ancients and that of the moderns, which is itself a product of their
divergent religions. The pagan religion was more conducive to politics because it considered virtuous those deeds that were likely to bring glory
to a man, whereas the Christian religion considers these pagan virtues
sinful:
Our religion has glorified humble and contemplative men, more
than active ones. It has placed its greatest good in humility,
abnegation, and in contempt for human things, while the [pagan
religion] places it in greatness of spirit, in strength of body, and in all
other things fit to make men very strong. And if our religion asks that in you there be strength, it wishes that you be fit to suffer more than to do a strong thing. (II 2)
Thus, Christianity "has rendered the world weak" because it teaches
that the state for which one must fight is "paradise" in the next life and
that this battle requires virtues very different from those that enable one
to glorify the homeland (II 2).8 In this manner, his explicit censure of
Christianity in this chapter accords with his treatment of Christianity's
"ambizioso ozio" in his preface to the first book. At this point, a return
to paganism's exaltation of the homeland appears to be the obvious
remedy. (Vickie B. Sullivan, Neither Christian nor Pagan: Machiavelli's Treatment of Religion in the "Discourses", Polity, Vol. 26, No. 2 (Winter, 1993), pp. 259-280 : 261-3.)
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Reading
Vickie B. Sullivan, Neither Christian nor Pagan: Machiavelli's Treatment of Religion in the "Discourses", Polity, Vol. 26, No. 2 (Winter, 1993), pp. 259-280.
Mark Hulling, Citizen Machiavelli, Princeton: Princeton University Press, 1983.
Rebecca Bamford, 'The Art of Power: Machiavelli, Nietzsche, and the Making of Aesthetic', Journal of Nietzsche Studies, No. 38 (FALL 2009), pp. 95-9.
Diego von Vacano. The Art of Power: Machiavelli, Nietzsche, and the Making of Aesthetic
Political Theory. Lanham, Md.: Lexington Books, 2007. xi + 215 pp. ISBN-13: 978-0-7391-1088-1.
It should be added that Sullivan does not fully endorse the account of Machiavelli given above, but the quotes and commentary speak for themselves.