Neither the Arab-Muslims of Palestine nor the Jews of the State of Israel (or elsewhere) are pure-bloods.
Both groups carry the genetic markers of the endless array of conquerors and contestants for the region over the past several thousand years.
And even with all that admixture, the Arab-Muslims of Palestine are probably more narrowly defined, genetically, than their Jewish antagonists.
Mostly because the Jews have been wandering for 2,000 years and have picked-up strong genetic markers from the Two-Rivers region (Bablylonian, Sumerian, etc.) and the Caucuses and Urals and Slavic and Mongol and Eurasian sources, as well as some heavy genetic contributions from Central and Western Europe over the past several centuries.
As I recall from earlier readings about the beginning-times for the Jewish Diaspora, Judaism was, for some considerable period of time, entirely embracing and welcoming of new converts from the lands into which they dispersed, to an extent where some Jewish ancestry-lines actually begin with a post-Diaspora conversion of Gentiles, rather than a maternal link all the way back to ancient Judea-Israel.
This, of course, forms the basis for objections that the Jews of today are not the inheritors of the Jews of Antiquity, and, genetically speaking, there seems to be some truth in that assertion; but, as with most things, it's only a Partial Truth, and, in many persons of the Jewish faith, we can, indeed, find genetic markers linking them to the Judea-Israel of Antiquity, so, that's pretty much a 'wash' - a mixed bag.
But such distinctions grow fuzzy and they lose some measure of importance in light of the mixed racial-ethnic genetic inheritance of the Arab-Muslims of so-called Palestine... part Arab Beduoin blood, part Western European crusader blood, part Hebrew blood, part Byzantine blood, part Roman Legionary blood, part Egyptian blood, part Berber blood, part Iraqi or Persian or Greek blood, part Ottoman Turkish blood, etc... like most folks on the face of the planet... mutts rather than pure-bloods.
So it comes down to Religion and Culture and Philosophy as much as race.
The Jews of modern-day Israel are the Cultural and Spiritual and Philosophical Heirs of Judea-Israel of Anquitity, and, after the slaughter of 6,000,000 of their men, women and children at the hands of Euro-trash during the Holocaust, the Jews decided to stop Wandering and to take back their ancestral and spiritual Homeland.
Nobody was going to hand it to them, and they'd been shoved-around for centuries up to that time, so, they chose to do some shoving themselves, for once, and to stop playing the victim-sheeple.
They succeeded beyond their - or the world's - wildest dreams.