Aside from Jews and Christians, religion in the Roman world as elsewhere was polytheistic. Generally speaking, most took their relationship with the gods seriously, as the plethora of religious holidays and festivals demonstrates. Some philosophical schools did consider the possibility of one supreme god who ruled all the other gods.
Of supreme importance in the Roman Empire was the cult of Rome and Emperor. Roma was the goddess of Rome; and the emperors in the imperial era were considered semi-divine, often “deified” by the Senate after their death. (Note that one could lose their “deified” status, as did the Emperor Domitian. This was done by an acta damnatio memoriae as is related in our story.
Christians in the principate of Nero became a criminal class: Christiani esse non licit: “It is not lawful to be a Christian.” Why?—because they would not accept or worship the cult of Emperor and Rome. That very refusal was treasonous, and treason is a capital crime—the sentence is execution. This is at the heart of the Christians perilous status, and was to remain so until the Emperor Constantine in 312 AD gave Christians legal status.
There was no organized persecution of Christians despite their criminal status until the latter part of the 2nd century. Persecution was sporadic and localized, but nonetheless deadly. The correspondence between Pliny as governor of Bithynia-Pontus and the Emperor Trajan in 111-112 AD is part of this story and illustrates the nature of legal-court proceedings when a Christians were arrested and sentenced.