I should expand on each point. The first is straightforward. One species in two places adapts and changes. The beginning of the change is often color as we see with birds. After some time the separation becomes permanent and you have two completely different species.
This happens often in other species. No reason to think humans are any different. Darwin noted this in finches.
The other element of this is Sephardim often react to Ashkenzim as "the other," which makes getting to Israel very difficult. An Ashkenzic Jew often finds in Israel that his neighbor is a Sephardi and then the Sephardi spends all his time and money and efforts to get rid of the Ashkenazi. This happens so much that you could say the main reason Ashkenazim do not make aliya is not the Arabs, but the Sephardim.