The Roman Empire was extremely valid in their fear of Christianity, the up rise of this new religion was against their way of life. Romans were obviously polytheistic. Christian views forbid them believing in more than one god, deeming them monotheistic. They were also forbidden from participating in rituals of the state religious cult. Christians when they decided to be Christian and not participate in the rituals were viewed as traitors and threatening the empire. The problem for Romans is that these rituals and are known and recognized to be essential for the continuation of the Roman State. This being stated, any Christian was seen as not loyal to the homeland nor the gods ruling it.
Speaking from the Roman perspective and experiencing the effect of this new religion on the empire, I personally would support stamping out this religion. Hypothetically if there was a new religion that threatened or we believed would destroy our government, we’d shut it down immediately. The group would be shunned and not tolerated in America (hypothetically). Depending on how a Roman defined danger to their empire would determine whether the Christians were a dangerous new cult. The rituals were very important to the Romans and if they were as vital to maintenance and continuation as believed, then the Christians were in fact a dangerous new cult. The Romans had a lot to lose allowing Christianity to become so prominent in their eyes.
Another huge issue Christianity caused for the Roman Empire is that is empowering to the lower classes of the society. The Christian belief system allowed the believers to not fear the power of the human and that any display could never touch their soul. Christians were no longer afraid of those above them in position and power, it was irrelevant to their soul no matter what happened to them. This was disgraceful to the Romans and they were deeply disrespected and unapproved. Christians were clearly shifting the power from “fear of the empire” back to the people and that no matter what happened, their soul was saved. Roman tenants of society were being ignored including love of power, ancestral social standing, glory of combat and a slave revolt was becoming much more likely with the rise of the new religion. The fear of a revolt was a constant worry to the Romans, it would be the ultimate downfall to their empire, when all in all, they could shut down Christianity and continue to reign until the next issued arose. Roman deities and high class wanted people the people to under their vulnerability and weakness to the power to they had but Christianity stripped this belief and allowed the believer some solitude beyond their physical being. The afterlife was praised and changed the mindset and perspective of many. This In turn, weakened the norms and social desires of Rome like power, glory, riches etc. Their fancy lifestyles and polytheistic ways had become irrelevant to their own people and they began to lack support at home.