To go beyond Nietzsche's philosophy I'm most familiar with Evangelical American churches. I don't see Nietzsche's thought meshing with them at all since, in general, theology essentially boils down to the precepts of:
1. All man kind is doomed to eternal torment.
2. Only faith in Jesus can save one from torment.
3. Salvation is by "faith alone," works are meaningless.
4. Once you are saved you are always saved.
These precepts are then taken to the logical conclusion, which is "go out and convert now! Convert! Convert! Convert! Everyone is doomed who doesn't accept Christ, but once they do they are good to go." You'll find churches where nothing else is preached aside from variations on this. There are, of course, variations in theology. For some, you can lose salvation through doubt, and for others, people who are not exposed to Christ don't go to hell. The latter creates the interesting contradiction where a generation could "take one for the team," and expunge Christianity from the world, thus saving all people from damnation.
However, I can see how elements of Nietzsche's thought could be worked in. If you look at his early work, particularly his Birth of Tragedy, you see the juxtaposition of the Appolonean (Aristotelian) mean and Dionysian ecstasy. The fact that, contrary to Nietzsche's bent, people tend to live happier lives cleaving to Aristotle's ethics of continence, the Appolonean, shows our fallen nature. Yet the ecstatic is the root of the religious experience. Nietzsche gets at something essential when he points this out.
I think our world reflects this simple truth. Hence the explosion of charismatic brands of Christianity, be they Pentecostal, or the new Catholic charismatic trend, big in Latin America today.
The conception of becoming more through overcoming does fit better with the Orthodox idea of salvation. Dostoevsky read and explicitly replies to Nietzsche with his Christian existentialism, and I'm happy I read the Brothers Karamazov soon after going through most of Nietzsche's work and Kaufman's excellent guide and biography. It's an able Christian response, the best I've seen.
Looking further afield, the idea of rejecting the morality of the world and chasing ecstacy and knowledge meshes fine with Gnostic Christianity, although Nietzsche clearly wouldn't agree with the asceticism of the Cathars or early Gnostics, or their Platonism. However, despite being so far off ontologically, they seem to fit together spiritually quite well.
The Gnostic pneumatic is similar to the Overman, stepping over conventional, worldly morals, and seeking truth above all else. They take a similarly dim view of the masses, of the great bulk of Christians and Jews as hylics. Nietzsche is obviously proselytizing for his ideas, so there are similarities there as well.
Nietzsche is writing about main stream Christianity in 19th century Germany and I never got the impression he studied theology let alone mysticism much, so his attacks won't bother all religious people. His description of Jewish morality is just going to seem surface level to the Jew steeped in Merkabah and Kabbalahism.