A useful book in this regard is Wilken's The Christians as the Romans saw them, which focuses on 5 early 'critics' of Christians. Broadly speaking, Christians were viewed as a novel sect that had anti-social and anti-imperial tendencies.

Generally speaking (I am giving you an overview), Romans perceived what is old as authoritative and reliable, what is new as dangerous and revolutionary. In this respect, Christianity had the double disadvantage of being a religious movement of very new provenance, and of not being associated with either a geographical or ethnic group. Thus, as it became distinct from Judaism, it became more troublesome.

Roman religious practice is, understandably, a complicated social phenomenon, but it's important to understand that it was tightly woven with socio-cultural mores and community orientation around your local settlement/town/city. To participate in religious practices was, in our terms, your civic duty. Christian dissension from participation in 'pagan' practices thus generally marked them as politically dissident, even if Christians didn't view themselves in those terms. Indeed, Christians regularly protested (in writing, I mean), that they were entirely loyal citizens of the empire.

This was further complicated by the development of the Imperial cult, particularly in the Eastern half of the Empire, in which devotion to the genius of the emperor and past emperors was practised as a form of divine honours on the civic level. Here, very explicitly, civic and religious duty was interwoven, and Christian non-participation was inclined to be taken as subversive.

On the question of violence - no. Because before Constantine the evidence overwhelmingly suggests that Christians did not practice violence on any significant scale. Almost all Christian writers assume a form of pacifism. Christian authors consider military service an inappropriate employment for believers. I would argue strongly that it's only in the 4th century that you begin to see the emergence of violence practiced, and justified with theological rationale, by Christians.

As said elsewhere, in ancient times and even relatively into the modern period, state and religion were difficult to tease apart. Those who didn't participate were seen as dissidents who might bring about a bad harvest, natural disasters, or ill upon the empire or the emperor. Such unpatriotic activities could even be construed as treasonous in our modern parlance. As documented in the letters of Pliny the Younger, who was an imperially appointed governor in today's northern Turkey, Pliny writes to the Emperor Trajan asking of how he handle the punishment of accused Christians:

Meanwhile, in the case of those who were denounced to me as Christians, I have observed the following procedure: I interrogated these as to whether they were Christians; those who confessed I interrogated a second and a third time, threatening them with punishment; those who persisted I ordered executed. For I had no doubt that, whatever the nature of their creed, stubbornness and inflexible obstinacy surely deserve to be punished. There were others possessed of the same folly; but because they were Roman citizens, I signed an order for them to be transferred to Rome. ...

... I therefore postponed the investigation and hastened to consult you. For the matter seemed to me to warrant consulting you, especially because of the number involved. For many persons of every age, every rank, and also of both sexes are and will be endangered. For the contagion of this superstition has spread not only to the cities but also to the villages and farms. But it seems possible to check and cure it. It is certainly quite clear that the temples, which had been almost deserted, have begun to be frequented, that the established religious rites, long neglected, are being resumed, and that from everywhere sacrificial animals are coming, for which until now very few purchasers could be found. Hence it is easy to imagine what a multitude of people can be reformed if an opportunity for repentance is afforded.

To which the Emperor Trajan basically says, "Yes, everything you did was fine. But we don't want to set a bad precedent at the same time; don't go witch hunting."

Source: Pliny book 10, letter 96; Latin version