The main reason why Christianity spread in the Byzantine Empire is that decades prior to the emergence of the Empire, Roman Emperor Constantine made Christianity the official religion of the Roman Empire, with they Edict of Milan, which he decreed in 313 AD.
We must remember that the Byzantine Empire is simply the Eastern Roman Empire, and when the Middle Ages started, the Byzantine Empire held land that had been christianizing for a over a century. Only a few areas of the Empire had to christianized in the Middle Ages, essentially areas at the edges of the Empire.
