The tradition of the popes wearing red shoes were carried over from the customs of ancient Rome itself. In fact, by the time of the Byzantine Empire only three people are allowed to officially wear red shoes in the empire: the Emperor, the Empress, and the Pope. Even in art, depictions of people wearing red shoes are severely restricted to the above-mentioned or the angels.
During ancient times, the manner and style of dress signified and symbolized rank, heritage, group or cultural affiliations, status, also of privilege. This was more true then than it is now. The manner and style of a person identifies him. For example, during the Yuan dynasty, only the Khan can wear green under pain of death. And during the Ching/Manchu dynasty only the Emperor can wear the Imperial yellow.
The toga, for example, was exclusively worn only by Roman citizens. The toga praetexta, furthermore, can only be worn by magistrates as this was a symbol of his office and rank. The republican senators wore red shoes, as did the Roman patricians. This custom was carried over from even before the Roman Empire, and before the Roman Republic tracing it back to the Kingdom of Rome. Thus this manner and custom of privilege of footwear is very ancient.
By the time of the Edict of Milan in 313 under Constantine the Great, Christianity was finally tolerated and the status of the Church enhanced throughout the Roman Empire. It was around this time that the bishops received the privilege of wearing the purple - a privilege still seen today. It was around this time after the toleration of Christianity and the transfer and donation of the imperial Lateran palace and Lateran basilica to the Bishop of Rome, (Pope Miltiades) and to the Church that privileges of imperial rank and imperial status are crystallized in the manner of footwear. Thus this privilege of red shoes can be (circumstantially, since firsthand written historical or archeological evidence have since been lost or destroyed by successive waves of barbarian pillage and destruction and looting during wars) traced at this point. The ancient Roman custom has now become Christian.
When the capital was transfered to Constantinople in 330, by political necessity the then suffragan bishopric of Byzantium was raised to an archbishopric. It was around this time that aspirations to greater status by the Archbishop of Constantinople becomes evident. Although only Rome, Antioch and Alexandria were patriarchates, by 381 a canon was inserted (and refused by the Popes) to establish the Archbishop of Constantinople as Patriarch. Political vicissitudes under the patronage of the Emperor, notably after 451 would later impress the status quo we have today by creating the Patriarchates of Constantinople and of Jerusalem. It was only after the Council of Florence in the 15th century that the Roman Church accepted the status quo of the Pentarchy. Although the Patriarchs of Constantinople have a history of trying to usurp authority and privilege during the Byzantine Empire, nevertheless, the ancient Roman privilege of red shoes were never extended nor granted to the Patriarch of Constantinople or anybody else in the Empire - a fact that remains to this day in life and iconography.