The Empire was Christian, of course. But nineteen centuries will lead to changes even in the Church.
The various crisis leading to the seven great ecumenical councils are well known and do not bear repeating. Nor does the great schism between the western and eastern churches.
Konstantinos X had insisted on religious unity within the Empire, and had forced the peoples of Armenia to agree to the orthodox creeds. His campaigns in the Levant restored the Patriarch of Jersusalem to the church.
Konstantios III’s campaign in Egypt restored several the Patriarch of Alexandria to the church. He had then asked the Pope in Rome to agree to rejoin the Pentarchy, but the Pope continued to insist on his authority over the other bishops. The resulting war was brief, and the Patriarch of Rome was given to a Bishop of the Greek Rite.
Soon after, the First Council of Rome was called, inviting bishops from all of Christendom. And bishops came from all over, except from the Holy Roman Empire, where the Pope had fled. Few bishops came from there. At the council, the differences between the Western and Eastern churches were reconciled. The authority of the Pentarchy was asserted, with the possibility of autocephalous patriarchs admitted, but with all such bishops in communion with the pentarchy and recognizing them as first among equals. The Latin and Greek Rites were both officially recognized, with more Rites recognized in later councils. The Filioque controversy was notably not resolved under pressure from Kosntantios to focus on the other issues, and largely grew to be a matter of local consideration. While not all bishops agreed with the Council, rulers across Europe mostly sided with it, and within fifty years most of Europe was solidly orthodox. The greatest exception was the Holy Roman Empire, where the few bishops who had gone to the council were eventually overridden. In that same time period, the HRE became staunchly catholic.
However, a century later, France’s king declared for Catholicism, and that nation quickly followed the HRE in converting away from the true faith. Over the next century, France would conquer England and spread the Catholic heresy even there. During that time the Empire continued campaigns against Muslims, and as their lands were brought back into the Empire they turned back to Christ. The later Mongol invasion of the Muslim heartlands and subsequent conversion to Christianity seemed like the death knell for Islam, especially given the Christian Reconquista of Iberia and the Imperial conquest of northwestern Africa. The Mongols had converted on acceptance of the Asian Rite within the Orthodox community, making it ever more diverse.
But even as the Empire brought the Mediterranean fully under its control, the HRE conquered Polish lands from the Golden Horde, converting them to heresy. And the Timurids swept into Persia, Arabia, and Russia, seeking to reclaim not just the old Islamic heartlands, but traditionally Christian lands as well. By the beginning of the 15th century, France had been conquered and converted to Orthodoxy yet again. By the end of the century, the Empire had conquered nearly all of England and had defeated the Timurids and replaced them with client kingdoms, again converting the peoples to orthodoxy. These client kingdoms often developed yet more new rites, which were accepted as orthodox.
The early 16th century saw the Protestant and Reform movements in Catholic lands. But Konstantios XI was a zealot, and on his ascension to the throne, he led the Empire to war with nearly all of the HRE, Catholic, Protestant, and Reformed all. Not only did this lead to the dismantling of the HRE, but to the various rulers being brought into the Orthodox fold. Of course, this led to even more new rites, even more different than those that had come before. The Protestants sometimes even used instruments in their worship.
With the end of the fifteen years war, the Empire soon found itself in contact with the Americas. In the areas where the Empire later colonized, the locals joined the churches in the new cities the Empire inspired. Whether this was part of their turning the Empire’s colonization efforts into local political organization or sincere conversions mattered little, the next generation was stanchly orthodox. But in the new world, there were even more new rites, incorporating local religious and cultural traditions into Christianity. More extreme were the rites in the organized polities that were never colonized. They accepted imperial missionaries (and the imperial advisors that taught them writing, metalworking, horsemanship, and gunpowder production), but insisted on their own autocephalous bishops and local rites. By now, the pentarchy had little power outside the eastern Empire, where the Greek Rite was used. Everywhere else had their own autocephalous bishops and slowly diverging Rites.
The conversion of the former Holy Roman Empire to orthodoxy took time (and occasional wars), despite the rulers having converted. But in time all of Europe and the Americas (and later Africa) were brought into religious communion, even if that communion was far more diverse than could have been imagined in A.D. 1000, let alone A.D. 33.
The Time of Troubles shattered that unity. When Burgundy declared its independence, it was under the lead of a man declaring himself the Pope. It was unknown if Catholics had remained underground for those centuries, with a secret and unbroken Papal succession, or if this history was fabricated as part of the rebellion. But he led Burgundy, allied with Italy, and they both won their independence. When the King of Italy died, the Pope proclaimed himself ruler of Italy, placing the Pope in control of Rome for the first time in eight hundred years. Where this would lead no-one knew.
In orthodox realms, the church tended to remain strong, though. Recent philosophers had begun to make atheism acceptable to believe, but it was not a widely-held belief. Some communist and fascist nations tried to remove the influence of the church, but this was new and had not yet taken a strong hold. So the church was quite influential in the early 20th century.