One often sees the question in my title posed, and also regularly sees generically affirmative or negative answers given to it.
However, the question–like many others of its kind–is nonsensical as framed. There is no answer to it.
Or, rather, there is an answer; and that answer is, “It depends.”
I would submit that the “subversiveness” of Christianity varies directly in proportion to the extent to which the state has been deified or has deified itself. Thus, in Hitlerite Germany Christianity was viewed as subversive of the dominant political order. The same was true in first and second century Rome.
We can see this quite clearly by looking at the famous letter (10.96) of Pliny the Younger to the Emperor Trajan in which he inquired what he, as governor of Bithynia and Pontus, should do about the adherents of what struck him as a bizarre new religion.
Pliny states that he had had an initial encounter with those denounced as Christians, executing for “stubbornness and inflexible obstinacy” those who would not (“whatever the nature of their creed”) recant. This initial action of the magistrate of course led to further denunciations of a group that made for good scapegoats (as they also did in the case of Nero’s fire in Tacitus’ account in Annals 15.44).
Pliny next tells Trajan what he demanded the accused to do:
“Those who denied that they were or had been Christians, when they invoked the gods in words dictated by me, offered prayer with incense and wine to your image, which I had ordered to be brought for this purpose together with statues of the gods, and moreover cursed Christ–none of which those who are really Christians, it is said, can be forced to do–these I thought should be discharged.”
Others first claimed that they were Christians, but then denied it and stated that “they had been but had ceased to be” Christians at various points in the past, and these too “all worshipped your image and the statues of the gods, and cursed Christ.”
Pliny was not particularly concerned with “the nature of their creed,” as noted above, except in so far as it impinged upon their public actions as dependents of Rome. That is, Pliny was concerned that they be good subjects of the Roman authorities, which entailed, not stubbornness and obstinacy, but obedience. They had to display their conformity and their willingness to submit to the magistrate by a simple act of paying homage to two kinds of images: that of the emperor and those of the gods. The emperor had been brought into the orbit of divinity and sanctified by its aura; disobedience to the emperor, therefore, was disobedience to the gods who underwrote Roman rule.
Pliny tells Trajan that he demanded in addition that the Christians curse Christ, perhaps because he understood that what he was asking vis-a-vis the images of Roman authority was incompatible with and exclusive of their claim to allegiance to Christ. To the extent, then, that Rome had appropriated divinity to itself, and had emperors who did not view themselves as “men under authority,” it was by necessity in open conflict with the claims of the Christian faith. And so she punished the adherents of that faith accordingly. Their faith made it impossible for them to be “good citizens” in the nature of the case, precisely because of the way in which the authorities had chosen to define in what good citizenship consists. In this instance, being a “good citizen” in one sense precludes being a “good citizen” in another.
There is no easy answer, then, to the question of whether the Christian faith is politically subversive; for the answer hangs almost entirely1 on the conception of political order in play in any given time or place.