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.