Isn't it strange that Cavafy lives in an Hellenistic way? Can we say that this is due to the absense of a real Church in Alexandria and/or a stronger appeal of ancient Greece there, precisely to non-Greeks?

Maybe it is so. Cavafy lives in the past, but not desperately. All periods of Greek history pass through his poems and become sources of advice and inspiration. This is not syncretism. Syncretism means a relative value - mainly in religious beliefs, but also in cultures at large. This doesn't happen with Cavafy.