What do you mean by Arabic areas? There were Christians in pre-Islamic Arabia, and quite a few Jews.

I’m not sure what you mean by Arabic areas. Do you mean the Arabian peninsula, or do you mean areas currently considered predominantly Islamic?

Well, as /u/talondearg said, Christianity did spread throughout areas which would later become 'Islamic' and beyond. In fact, one of St. Paul's first missions was to Arabia, although it was largely unsuccessful. In the 6th century, Christianity almost swept across the Arabia peninsula by force. The northern Ethiopian kingdom of Aksum likely converted to Christianity in the 4th century, and subsequent Christian monarchs became enthusiastic defenders of the faith in the region. By the 6th century, the Yemeni city of Najran was a major hub for Miaphysite Christians, many of whom were seeking refuge from the Byzantine Empire. In 523 or 524, the local king, Yusuf as'ar Yath'ar, inflicted a terrible massacre upon the local Christian population, provoking an intervention from the Aksumite King Kaleb, who then set up a Christian client state in southern Arabia. This Christianised Yemeni kingdom might well have expanded across the entire Arabia Peninsula, if it weren't for the ecological disaster that followed the collapse of the Great Dam of Marib, upon which agriculture in the region depended. This catastrophe precipitated the collapse of the Aksumite Empire in Arabia. Had the dam remained, the future Prophet Muhammad might have been born and raised a Christian, and history would have been very different indeed.