Okay so I know that the main conflicts in the middle east stem from the creation of a Jewish state, taking that land which had originally been Muslim. But why don't we see this kind of persevering tension with Christians regarding Turkey? Anatolia had once been the center of the Byzantine Empire, a great Christian empire. So is there any similarity between "the Jews taking Israel from the Muslims" and "the Muslims taking Turkey away from the Christians"?
Your main premise is flawed. The creation of Israel caused the conflicts between it and their neighbours in '67 and '73 (but arguably if Israel didn't exist, the regimes of the countries in the region might have anded up fighting each other anyway in petty border wars/sectarian conflict (as Iran and Iraq did from '79-'89) and obviously the continued occupation has kept the area of Israel and the Occupied Territories in a state of virtual pepetual conflict. However, the region is extrordinarily complex even without Israel (take a look at tiny Lebanon and try to work that one out!), especially with a history of minority regimes ruling majority populations (Syria is a prime example of this at the moment). As with so much, Israel's existance can often be used as an excuse for conflict or Israel's involvement in a conflict is just part of a greater whole of external interferance (Lebanon Civil War for example).
As for Anatolia, remember that there wasn't much in the way of population movement. The main way that Islam took over the former Byzantine Empire was by conversion rather than huge population movement (which historically what both Islam and Christianity has done in the 'Old World').