One of the best early Christian perspectives on theatre comes from Augustine of Hippo (354-430 CE); especially in his Confessions and The City of God. Though Augustine was writing from the later years of Roman Imperial power/influence, he takes on criticism of theatrical entertainments that were popular throughout the Roman world. Furthermore, the Roman/Latin Theatre of his day was still very much an 'inheritor' of the Greek Theatre, borrowing heavily from the form and aims of Greek tragedy and comedy. So, to answer your excellent question, I will consider Latin dramas and the Roman Theatre of the late Imperial period as a "descendant" of the Greek theatrical tradition. Indeed, many theatre historians and works on theatre history consider the Greek and Roman periods back-to-back as if they were both operating from a largely unbroken literary and performative tradition (see the authoritative textbook on theatre history: History of the Theatre, Brockett & Hildy).

Augustine of Hippo was an incredibly influential writer/thinker/theologian in the early history of Christianity and provided significant intellectual influence on the early structural development of the Roman Christian Church in the latter years of the Roman Empire. His ideas and writings survived well into the European Middle Ages, even serving as a significant source for the early medieval scholar and writer, Isidore of Seville. But, in his own day, Augustine provides one of the best educated perspectives on early theatre that has survived to our time. For example, in Book III of Confessions (https://www.gutenberg.org/files/3296/3296-h/3296-h.htm) he explains: "Stage-plays also carried me away, full of images of my miseries, and of fuel to my fire. Why is it, that man desires to be made sad, beholding doleful and tragical things, which yet himself would no means suffer? yet he desires as a spectator to feel sorrow at them, and this very sorrow is his pleasure. What is this but a miserable madness? for a man is the more affected with these actions, the less free he is from such affections. Howsoever, when he suffers in his own person, it uses to be styled misery: when he compassionates others, then it is mercy. But what sort of compassion is this for feigned and scenical passions? for the auditor is not called on to relieve, but only to grieve: and he applauds the actor of these fictions the more, the more he grieves. And if the calamities of those persons (whether of old times, or mere fiction) be so acted, that the spectator is not moved to >tears, he goes away disgusted and criticising; but if he be moved to passion, he stays intent, and weeps for joy."

Augustine is clearly taking an Aristotelian understanding of theatre--in which Aristotle explains that theatre (namely tragedy) serves as a purgation of emotion, experienced through what he calls 'catharsis' (κάθαρσις). But Augustine essentially questions the purpose of theatre and why a person would be (and, indeed, why he was) drawn to such entertainments? What is it about man's nature that brings him to such representations and audiences to the desire to watch these representations--especially if, after all, they are but false and fleeting shows of those things that are or may have been a reality. For Augustine, the theatre serves to engage human emotion in a weak attempt to capture that which the soul truly seeks: connection to that which can change the soul for a greater, more eternal purpose than the pagan-based, and ultimately false, stories of Greek and Latin tragedy. In "The City of God (https://www.gutenberg.org/files/45304/45304-h/45304-h.htm), Augustine takes his criticism of Roman Theatre a step further: using it as an example of civic activity dedicated to false (or empty) gods that corrupt a populace rather than uphold a connection to that which binds all of humanity: the soul's longing for the Truth of God. This is largely influenced by a popular belief that, after the sack of Rome by the Visigoths in 410 CE, the adoption of Christianity had led to Rome's inability to support its populace and protect the city from hostile foreign forces. Augustine uses Rome's own history--wherein theatres were largely banned in the city by influential leaders and politicians--to explain that even that Rome had, over time, had given itself more to the desires of the flesh (a City of Man) as opposed to the desires of the soul (the City of God). Ausgustine writes in City of God I.32: "And in this pestilence these gods find great enjoyment, because it benighted the minds of men with so gross a darkness, and dishonoured them with so foul a deformity, that even quite recently (will posterity be able to credit it?) some of those who fled from the sack of Rome and found refuge in Carthage, were so infected with this disease, that day after day they seemed to contend with one another who should most madly run after the actors in the theatres."

So, to summarize, Augustine wasn't necessarily writing a polemic against Roman Theatre, nor was he saying that theatre was inherently bad. But theatre, for him, was a weak attempt at reaching for the kind of emotional and cathartic needs of the soul that could only be found in the worship of the Christian God. Essentially, Rome showed itself happy to stop at merely entertaining shows that supported its own gods/desires/needs, while those that could put aside the attending the theatre in favor of attending church were seeking the City of God (i.e. a more eternal and fulfilling purpose) rather than the City of Man.

Aside from Augustine, there is another source that serves as a perspective on theatre of Roman world, but in a much more polemical way: John Chrysostom (c. 349-407 CE), Archbishop of Constantinople. Chrysostom was a contemporary of Augustine, but was living and operating from a different geographical and theological perspective. As the Archbishop of Constantinople, Chrysostom was closer (geographically and linguistically) to the center of Greek Theatre (Athens) and, in his sermons, was clearly familiar with the theatrical practices of the eastern Mediterranean. In fact, he rails against the base, highly sexual, and degrading spectacles of theatre in his area in his homily, "Against the Circuses and the Theatre" (http://www.tertullian.org/fathers/chrysostom_against_theatres_and_circuses.htm). In this homily, Chrysostom analogizes the theatre as a prostitute, drawing on the metaphor of the Church as a bridegroom to Christ, that corrupts and destroys the relationship between the lover and the loved. In his assessment of the theatre--which is far more polemical than Augustine--it is a destructive activity with no cultural or social value for Christians that seek a true relationship with God. He goes so far as to say: "Therefore I make this proclamation, in a clear and loud voice, that if anyone after this exhortation and teaching deserts back to the unlawful disgrace of the theatre, I shall not receive him within these precincts, I will not let him share in the sacraments, I will not let him touch the sacred table. Just as shepherds separate the sheep that are afflicted by mange from the healthy sheep, so as to prevent the rest from catching the disease, so I shall act in the same way."

But, for historians, Chrysostom serves as an excellent source of early theatrical entertainments. He describes a "water ballet" that took place at Antioch, in which nude women were involved in some sort of performance involving a flooded theatre. Indeed, [archaeological excavations of theatres in modern-day Syria] (https://en.wikipedia.org/wiki/Roman_Theatre_at_Apamea) and other parts of the Eastern Mediterranean world show that many had plumbing systems capable of bringing water into the theatre. What they performed and why is still a mystery, but Chrysostom's polemics help us construct an idea of the kinds of theatrical entertainments that were popular in different parts of the Roman world.

Overall, I think it's easy to say that the early Christian perspectives on theatre were not overly positive--though, that's not to suggest that Christians didn't attend the theatre. Rather, we should explain that theatre was a part of the social and cultural fabrics of the places in which it was practiced--as were Christians that lived alongside these theatrical entertainments. In many ways, the Christian populations of the Roman world took differing perspectives on the importance and influence of theatre in the early part of Christianity's public appearance within in the Roman world.

More information: Theatrical Shows and Ascetic Lives: John Chrysostom's Attack on Spiritual Marriage by Blake Leyerle (2001).