St. Athanasius’s LIFE OF ANTHONY says that St. Anthony headed out into the desert because of the influx of wealthy pseudo-Christians into the Church in the wake of St. Constantine’s conversion. Soon enough, many other people followed him, and the monastic tradition was born. We find in the homilies of St. John Chrysostom in Constantinople decades later criticism of women who came to church services wearing fortunes dangling from their ears; St. John believed there were better uses for that wealth with poor people in the streets.
Accommodating war was a difficult question for the Church. St. Constantine himself apparently waited to be baptized on his deathbed because he believed that a prince likely would have to do things inconsistent with his understanding of a Christian. Also at Constantinople, St. Symeon the New Theologian wrote in the 11th century that Christians should avoid political power, because it was bound to corrupt them. In Russia, according to the Primary Chronicle, St. Vladimir followed his conversion of his kingdom to Christianity with abolition of capital punishment. The Chronicle says the bishops soon went to him and begged that he restore it, because crime was proliferating. In medieval Constantinople, soldiers who killed even in defensive wars were required to do years’ penance before receiving the Divine Gifts again. The Kievan Grand Prince Vladimir Monomach demonstrated a powerful sense of his spiritual obligations in his letter to his sons, and this attitude runs through the history of Russia in particular. For example, the 19th-century emperors Nicholas I and Alexander II devoted themselves to constant travel around their gigantic empire in service to the nation. Nicholas supposedly took care personally to ensure that attendees at the divine services stood in the right place, lit candles at the right time, etc. Constantly.
As far as the doctrine of the Church goes, it happens that I wrote a brief article in THE GREEK ORTHODOX THEOLOGICAL REVIEW about 15 years ago on Eusebius’s treatment of the historic role of the emperor/saint Constantine in his historiography. The Church never required one to subscribe to Eusebius’s view of history, but one certainly sees it reflected in writings of Orthodox churchmen through the medieval period and down nearly to our time. The famous Imperial Russian notion of Moscow as “Third Rome” (“Two Romes have fallen, Moscow is the third, and a fourth there shall never be”) captures it. So does Orthodox recognition of numerous Christian princes — Constantine, Theodosius, Justinian, Vladimir, Alexander II, Nicholas II, Alexander Nevsky, and others — as saints.
There once were parish churches in Western Europe named for St. Constantine too. It has been over a decade since I paid much attention to these questions, so I don’t recall whether they still bear his name. (I don’t mean only at Ravenna.) This tradition was of course a casualty of events at Rome beginning in 800. From St. Constantine’s day, or, if you want, from Eusebius’s, the eastern Church saw “symphonia” as normal. Only in the west, with the abnormal experience of being conquered away from the Empire by barbarians in the 6th century, did the bishops come to insist on independence of the emperor. Of course, either approach can be problematic.