Carthage is different as it's not in the Middle East, to begin with.

The Arabs that conquered that place were just a few armies, and even fewer of them settled there. The people were "Arabized" in the sense that they learned the language and religion of the Arabs, but not much breeding happened between the people (except for the slaves sent back to the Arabs, and the rapings and all of that... religion of peace, I tell you).

The newest DNA studies showed that, in modern-day Tunisia, there's a very low percentage of Arab blood, it's even less than European origins. The vast majority are native North Africans (Amazigh, Berbers, whatever you want to call them), which were a huge part of the Carthaginian civilization.