A systemic, organized movement of Christian believers fully emerged during the height of the Roman Empire. Pontius Pilate, a Roman governor of Jerusalem, executed Jesus by crucifixion sometime around 30 CE, and Christianity became officially outlawed shortly thereafter. We know that the Roman emperor Constantine would eventually convert to Christianity in the year 312 CE, but the time in between the death of Jesus and Constantine’s conversion was one of struggle and tribulation for the fledgling Christian community. It was into the polytheistic religious landscape of the High Roman Empire that Christianity would have to compete for dominance.
Early Christians faced extensive persecution by the Roman military because the period between roughly 1 CE to Constantine’s conversion was one in which the Roman emperor ruled through imperium, which literally translates to “command” but was generally used to refer to his absolute and unquestionable authority. The reason this was problematic for the early Christians is because Christian belief, which gradually became formalized through the travels and teachings of various Christian apostles (most famously Paul of Tarsus), held that true believers of the faith would not worship any earthly entity; rather, they could only recognize the supreme authority of God and his son, Jesus.
For the Roman emperor, most of the practitioners of polytheistic religions at the time did not pose much of a threat, because many of these religious belief systems could tolerate the subordination of their various deities to the authority of the emperor. The emperor saw himself as a kind of father who benevolently ruled over his people as his own family, but whose patria potestas, or “power of the father,” was unchallengeable. Christians challenged exactly that, and for that reason, they were persecuted.
Another reason why early Christians were so rigorously persecuted was because the worship of various saints—and the aesthetic lifestyles that usually accompanied this worship—threatened the entire social order that the Roman Empire was built upon. There is an excellent book about this by the historian Peter Brown called The Cult of the Saints, in which he argues that the emerging practice of relic worship convinced many devout Christians to leave the traditional patrician-plebeian networks to accept the anthropomorphized saint as their new patron. This was disastrous for Roman society, because Rome and many other large cities began to lose large portions of their tax-paying populations to what was (at the time) a seemingly whimsical religious cult.
Therefore, the early Christians were born into an incredibly hostile religious landscape. Fundamentally, they can be distinguished from the followers of Judaism at the time because the Roman government generally tolerated the Jews. This was because Judaism, which does not glorify the human being Jesus Christ over the authority of the emperor, did not threaten the overlying social order, and Jews were often willing to cooperate with Roman political and social norms.