Don't get hung up on "Arab". It is a cultural and linguistic distinction, not a racial or genetic distinction. A Berber in Algeria or an Arabian (Bedouin) from the Arabian peninsula is nothing like a Levantine from Palestine or Lebanon. They just speak the same language and share literature, foods etc.
While many people in Palestine had already converted to Christianity before 380 AD, after 380 AD, the Roman Empire made Christianity the state religion. Most non-Christians throughout the empire converted to Christianity. In the province of Palestine, because of its importance to Christianity, to be a resident one had to be a Christian. Hence, permanent residents were Christians that had converted from other religions, including Judaism.
Besides residency requirements, Emperor Theodosius I issued heresy laws, which made it imprudent to practice any religion but Christianity.
"We command that those persons who follow this rule shall embrace the name of Catholic Christians. The rest, however, whom we adjudge demented and insane, shall sustain the infamy of heretical dogmas, their meeting places shall not receive the name of churches, and they shall be smitten first by divine vengeance and secondly by the retribution of our own initiative, which we shall assume in accordance with divine judgement."
The Christian Church and the Persecution of Heretics
"Almost overnight, Christianity was propelled to the status of global, theological powerhouse. Roman citizens and subjects converted in droves, as Christians were afforded special tax breaks and other amenities not available to any other religious affiliations. Despite its favored status, other religions were now outlawed by Constantine. It would not be until later in the 4th century (380), when Christianity would be named the official state religion of Rome, illegalizing all other models of worship. ................................Failing to convert typically elicited deportation or execution."
How Christianity Rose to Dominate Europe