Greco-Roman Religions might be considered “the competition” of early Christianity, but this is not a fair description of how religions functioned in the first century.Some of the papers at the St. Andrews Symposium on Divine Sonship last June dealt with this topic.
First, in the first century, religion was rarely a choice. A person owed worship to a god because of a civic or family obligation or because the god is associated with a trade. A person living in the Roman world would not even think in terms of “converting” from one god to another, since gods had various functions; motivations were purely practical. If one was going to sea, one appeased sea gods. In fact, the idea of choosing to worship a particular god was the attraction of the mystery cult. One might become a worshiper of Mithras by choice, although obligated to also worship other gods.
Past posts in Phil Long's series on the Second Temple Period are noted here and links.