Throughout history many Jews converted to Islam or Christianity. Same goes for Christianity to Islam and vice versa. Moreover many Christian Arab tribes settled in the Levant.
Therefore religion doesn’t define the gene.
1) No Jew or Christian ever just converted to Islam in the Middle East, they were CONVERTED BY FORCE. And after they were converted and the Arab identity was forced on them they became Arabs and started mixing with other Arabs from all over the Arab world.
2) No Muslim ever converted to Christianity simply because that would be considered apostasy and would mean their death, since you know Christians are considered infidels that will burn in hell forever according to Islam.
3) Christian Arab tribes didn't exactly settle in the Levant per se, and most certainly not in Lebanon. They lived on the Levant-Arabian border in places like Jordan and the Syrian desert. And they were the first ones to be killed or converted by force during the Muslim conquest. Further proof of that is that the supposed descendants of Christian Arabs, the Christian Orthodox, are genetically no different from the Syriac Maronites.