Then they are no longer "ancient people", they are assimilated Arabs, as they took their politics, religion, culture, language, identity, even interbred with them.
Much like the descendants of Samnites are simply Italians, not Romans nor some "ancient people".
You may aswell try separate the descendants of Vistulans out from the Polish nation.
All interbred with each other at some point or another. As i said, especially in that region, genetically pure groups are very rare and neither of those is even close to that.