What did Romans think about the persecution of Christians?

Answer 1

There is no real evidence of the Romans persecuting Christians before at least 97 CE, and only sporadic periods of persecution even after that. A Christian tradition holds that Nero persecuted the Christians living in Rome because he blamed them for the Great Fire, but historians have been unable to find any evidence of such persecution or even a reason for Nero to want to blame them unjustly. If the story of the martyrdom of Stephen is based on fact, then that instance involved Jews, not Romans.
When it occurred, persecution was usually because Christians refused to worship the gods, thereby risking divine wrath. Some Romans felt that the gods could be appeased by punishing Christians who overtly refused to worship them. Sometimes emperors supported one side or the other for political reasons.

From the late fourth century onwards, Christianity had become the official religion of Rome and was in a position to persecute pagans and Mithraists. It seems that persecution does not choose its victims - whichever religion is more powerful at the time persecutes the less powerful.