Does it matter? Secularization isn't going to happen in the foreseeable future, anyway. Israel wants to preserve its identity as a Jewish state, and its Ultra-Orthodox minority has outsized influence as it is. And in most of the other states in the Middle East we see a rise in Islamism.
And if we could magically secularize somehow, I'm not convinced that it would make a big difference--tribalism and nationalism are a big factor now, and might well be more than enough to maintain the antagonism even without assistance from religious zealotry.