If the US and Europe pulled out of the Middle East it would be too chaotic to predict anything. It depends on the presence of other superpowers (Russia, China) and the pecking order that would be established between the regional powers (Turkey, Israel, Iran, Egypt + the Sunni world).

Also, "pulling out" is too simplistic. There are not only troops on the ground, but also military bases, joint exercises, weapon sales, commercial ties, industrial ties, scientific collaborations, cultural influences, and so on and so forth. Short of disappearing from the globe the US cannot just 'pull out'