Sorry to but in here again amongst the scholars and academics (and thanks, everyone, I am learning a great deal here!),but back to the historical 'what happened' question -
I live in Cyprus. Paul and Barnabas (who was a Cypriot) came here in about 45 AD and allegedly converted the proconsul Sergius Paulus. Cyprus thus became apparently the first place under a christian ruler. But at the same time, worship of the previous gods continued, especially that of Aphrodite (indeed, many church festivals here today are based on the Aphrodite cult. Kataklysmos is a good example. Held by the church to be a commemoration of the Flood, it's actually a celebration of the birth of Aphrodite from the sea).
The Jewish rebellion of 116AD hit hard on the island (there was only a small Roman garrison) and virtually the entire gentile population of Salamis (Barnabas' home town) was killed. When the rebellion was put down, all Jews were expelled from the island.
But christianity developed only slowly, alongside other religions. Most of the mosaic floors at Paphos (a short walk from where I live) which celebrate the ancient gods were completed in the late 3rd/early 4th centuries AD - i.e. only a very few years before Constantine designated christianity as the 'preferred religion'. Some of the catacombs were used in turn by pagans, jews and christians.
So there never was an 'overnight transition' as I had innocently once believed. Christianity developed alongside other religions and there was (I suspect) far more of an interchange between them than 'fundamentalists' might realise or suspect.