History. They share a long history with Muslims, having lived side by side for well over a thousand years.
Religion is of course different.
Most "Arab" Muslims in Israel, Lebanon and Syria are probably descended genetically primarily from the same people as the Christians. Arab or Aramean or whatever you choose to call them.
Most of the Muslims are descended primarily from converts from among the natives, not from invaders from the Arabian Peninsula.
However this shared 1,000 years of history has been the kind of history most indigenous people "share" with their conquerors. The Arabs Muslims (or, rather more predominantly the Ottomans) impose the jizya, the Aramaeans pay it. The Arab culture waxes, the Aramaean wanes. The Arabic language becomes dominant, the Aramaean disappears. Maps show an Arabized cartography; Aramaean landmarks and place-names are forgotten. The Arabs write the history, the Aramaeans lose their destiny.
Wanting to extricate themselves from that "shared history" -- that I understand.
>Most “Arab” Muslims in Israel, Lebanon and Syria are probably descended genetically primarily from the same people as the Christians.
In part, yes. However, the Muslims are still partly also descended from Arab settlers-such as the conquering caliphate soldiers who settled down and took wives and mistresses from the native population, and also from Arab tribes who settled or were settled in the area.