They used force
Through most of their history the ancient Romans had their own religion: Roman Religion. In the Later Empire Christianity spread in the Roman Empire, was endorsed by the Roman emperors and became state religion.
Christianity did not easily spread through the Roman Empire. See the related question, "How did Christianity spread throughout the Roman Empire?"
When Christianity was endorsed by the Christian Romans Emperors, these emperors appointed Christian senators.
By 325ad Christianity had spread throughout the Roman Empire and to Britain. If you google "spread of Christianity map" you will find maps showing the spread.
Slaughter and suppression of other religions, and it provided a religious hierarchy of bishops which was valuable for emperors to use as a control measure to supplement his secular power.
Christianity
The Romans did not try to stop the spread of Christianity. There were alternations between periods of toleration and periods of persecution. Some Roman emperors thought that Christianity was a threat to the Roman state because many bureaucrats and soldiers converted to Christianity. The Romans saw their state as being interlinked with Roman Religion. The persecutions were aimed mainly at the civil service and the Christian clergy, rather than Christianity as such. The last and worse persecution, the Great Persecution, failed because it was difficult to implement, because of the resistance of the Christians and because it undermined the stability of the empire. After that, the emperors endorsed Christianity, favored it over other religions and promoted it. Eventually, Christianity became the state religion of the empire. With imperial support, the spread of Christianity accelerated.
No. They fed Christians to lions for entertainment!
No. In fact, for hundreds of years the Roman Emperors did everything humanly possible to surpress Christianity. Until Emperor Constantine, Roman Emperors absolutely hated Christianity. The idea that a Caesar invented the story of Jesus is ludicrous.
The spread of Christianity had political ramifications for the Roman Empire. The empire split into two, Constantinople to the east and Rome to the west
Your question can be answered with two Roman emperors, depending on what you mean by accept. Constantine made Christianity legal, which made it an acceptable religion. Theodosius I made Christianity mandatory, which meant that everyone had to accept Christianity.Your question can be answered with two Roman emperors, depending on what you mean by accept. Constantine made Christianity legal, which made it an acceptable religion. Theodosius I made Christianity mandatory, which meant that everyone had to accept Christianity.Your question can be answered with two Roman emperors, depending on what you mean by accept. Constantine made Christianity legal, which made it an acceptable religion. Theodosius I made Christianity mandatory, which meant that everyone had to accept Christianity.Your question can be answered with two Roman emperors, depending on what you mean by accept. Constantine made Christianity legal, which made it an acceptable religion. Theodosius I made Christianity mandatory, which meant that everyone had to accept Christianity.Your question can be answered with two Roman emperors, depending on what you mean by accept. Constantine made Christianity legal, which made it an acceptable religion. Theodosius I made Christianity mandatory, which meant that everyone had to accept Christianity.Your question can be answered with two Roman emperors, depending on what you mean by accept. Constantine made Christianity legal, which made it an acceptable religion. Theodosius I made Christianity mandatory, which meant that everyone had to accept Christianity.Your question can be answered with two Roman emperors, depending on what you mean by accept. Constantine made Christianity legal, which made it an acceptable religion. Theodosius I made Christianity mandatory, which meant that everyone had to accept Christianity.Your question can be answered with two Roman emperors, depending on what you mean by accept. Constantine made Christianity legal, which made it an acceptable religion. Theodosius I made Christianity mandatory, which meant that everyone had to accept Christianity.Your question can be answered with two Roman emperors, depending on what you mean by accept. Constantine made Christianity legal, which made it an acceptable religion. Theodosius I made Christianity mandatory, which meant that everyone had to accept Christianity.
The Roman Empire was the geographical factor which first helped the spread of Christianity. It started in Judea, which was part of the Roman Empire. It was spread through this empire, especially its eastern part by Christian preachers. Originally the Christians were Jews who preached other Jews and followed Jewish law. Paul created a theology which opened Christianity to the gentiles (non-Jews) of the Roman Empire. He said that faith in Jesus and following his teaching was what was required for salvation. Therefore, you did not have to be a Jew or follow Jewish law to be a Christian. Christianity was endorsed by all but one of the emperors after Constantine the Great. This helped his spread. The co-emperors Gratian and Theodosius made mainstream Christianity (the Latin/Western Church and the Greek/eastern Church, which later came to be called Catholic and Orthodox respectively) the sole legitimate religion of the empire.