I don't think Judaism has much to do with any genes. Jews from all over the world pretty much adapted to the looks of the people they lived together with, implying a lot of intermarriage or at least mixing, as the number of converts was rather low. The same mixing should logically be true for the people in the places they were at, especially considering converts.
Additionally, it would be difficult to reduce Judaism to the few people fleeing Egypt and founding Israel. All the monotheist groups (tribes, cities...) sharing the same basic believes in and around the area should also be included, especially as some of them became "completely" Jewish when competition between different religions forced to take sides (Khazaria). That would include Slavs, Caucasians, Turk people, Arabs, and Egyptians. The Celts were pretty mobile at the time, so that influence can also safely be assumed. And since the people started to come to Israel from all over the world, German and African "blood" is also included. Pretty much the same mixing is true for basically all people on the planet, btw. - except a few isolated people like the Aboriginies. Sure one might be able to find genes that appear more often in one group than another - but it'll be difficult to find Genes which exclusively exist in nearly every member of one group - and most of the ones carrying such "markers" sure also have more common genes, or even genes usually appearing more in other groups.
As for the splitting up: I'm still a supporter of a united Israel including different orthodox and moderate states of both confessions, and secular states. It would include the West Bank. Looking at a map, I'd probably make the north (including Haifa), the South, and Jerusalem secular and the West Bank mostly Muslim (south moderate, north conservative). The remaining west coast is divided in a moderate south and an orthodox north. This way, orthodox Muslims and Jews share a border, but according to my experiences with religious fundamentalists, they'll get along very well. To match opinions with geography, I'd declare my intentions and encourage the people to use job changes, home changes, and the likes to choose also by their believes. I'd also sort immigrants accordingly, put ex-soldiers, ex-inmates and other suitable people in the areas of their choice, relocate police, administrative staff and so on accordingly, and so on. People are also encouraged to look for good spots for new businesses or for new jobs in their preferred area first. Sizes of states might change over time according to population, so that popular states grow and unpopular states shrink. But only when this is possible without people feeling forced to move - areas with indifferent or no people, areas where the people already created according facts by moving there, and so on. I'd also use this "everyone gets the state he likes the most" approach to get more immigrants from Arab countries, to have more Palestinians return, and so on - I'd say everyone advocating democracy, human rights, and so on, tolerating Judaism, identifying with Israel, and speaking Hebrew is sufficiently integrated to allow growth without loosing the essential identity.