The transmission of Classical Culture in Christian times is a vast topic. Some were copied for aesthetical purposes, others for allegorical, others for rhetorical purposes. Many continued to have immense prestige, even after Christianity had become the official and sole religion. A nice comparison would be to note that one doesn't need to be a Christian to hold the opinion that Paradise Lost is one of the richest texts ever written in English.

Homer was held in a similar esteem in the Greco-Roman world, and this includes Byzantium (and of course no one doubted that the Hymns were written by Homer). There are times of contention against these works, naturally, and there are also times of recovery and a renascent interest in the culture and texts of pagan Antiquity. Anthony Kaldellis argues in his Hellenism in Byzantium that, as the star of the Ottoman Turks rose, the diminution of the empire into the lands that had formerly been Greece, and so the retreating "Romanhood" of Byzantium, led to a re-identification of Byzantium with its Greek, rather than Roman roots, and also, in a sense, checking its Christian identity (though its centrality was of course never questioned).

I suggest the following books for further reading:

Anthony Kaldellis' Hellenism in Byzantium

Nigel Wilson's Scribes and Scholars

Jean Seznec's The Survival of the Pagan Gods