Nietzsche meant that Kant established the validity of Christian morality by making philosophical arguments that didn’t rely on Christian beliefs.
In The Gay Science, Nietzsche writes:
Kant wanted to prove, in a way that would dumbfound the common man, that the common man was right: that was the secret of this soul. He wrote against the scholars in support of popular prejudice, but for the scholars and not for the people. [§193.]
Kant held that all rational persons have an a priori understanding of the basic principles of morality. These consist of duties, both to oneself and to others, and above all the duty to respect rational agents. Most persons, however, do not understand that morality is a priori, and their moral commitments are therefore vulnerable to corrosive skeptical criticism. In The Metaphysics of Morals Kant formulates the ultimate standard for moral judgment, namely universalizability, and establishes the rational necessity of morality.
In Nietzsche’s view, Kant’s a priori moral principles are nothing more than the prejudices of traditional German Protestantism:
The Protestant parson is the grandfather of German philosophy…. The theologians’ instinct in the German scholars divined what [Kant] had once again made possible. […] The conception of a “true world,” the conception of morality as the essence of the world … were once again, thanks to a wily and shrewd skepticism, if not provable, at least no longer refutable. […] Kant’s success is merely a theologian’s success…. [The Antichrist §10.]
Nietzsche especially disliked Kant’s idea that moral motivation consists in respect for a universal concept of virtue:
A virtue must be our own invention…. The fundamental laws of self-preservation and growth demand … that everyone invent his own virtue, his own categorical imperative. […] How could one fail to feel how Kant’s categorical imperative endangered life itself! The theologians’ instinct alone protected it! [§11.]
There’s a sense in which all philosophers except Nietzsche have been theologians in disguise, in that they all claimed to be selfless, altruistic seekers of truth and goodness. Socrates, Nietzsche thought, was really doing what was good for him when he claimed that it would be good for everyone to examine their lives. It’s only with Nietzsche – in Nietzsche’s view, that is – that the philosopher removes his mask and publicly proclaims that his philosophical activity is in the service of his will to power.
Below, Martin Luther, theologian.