Israel's still around in 2080, which means the Middle East conflict is probably still raging on after a century and a half.
Not really. The establishment of a Palestinian state early in the timeline really does a lot to end the conflict. It doesn't end entirely, though, until the Conservative Insurgency of the mid-century finally peters out.
I read about the conflict in the Middle East with the “Conservatives” but what exactly does that mean? Conservatism in the region could range from anything like theocracy or monarchy to military junta or flawed democracy. Are you implying that the Arab Spring continues and rejects all of those?
I wrote that part before the Arab Spring started, but think of it as the next generation's backlash against it. Whereas the Millennial Generation pushed for liberalization and democracy, the Spectro Generation (what we call Generation Z today) in the Middle East ends up feeling it all went too far and you see a resurgence of conservative (not necessarily fundamentalist, but more religious) Islamic values amongst the young…kind of an inverse of the '60s generational divide in the US. There ends up becoming widespread disatisfaction with where their parents and Western-style capitalist democracy has taken them.
By 2031 tensions start to flare up again between these young Conservatives and the “Reformist” (moderate/liberal Islamist) establishment over high unemployment, a result of the weakening regional economy (an early sign the world was approaching Peak Oil), in the form of mass protests and militia violence. This starts in Syria and Lebanon but soon spreads to Jordan, Israel and Palestine, which leads to Israel considering a military intervention in Syria, which of course pisses off the Iranians. Attempts by the governments involved to break up the protests backfire, radicalizes the movement, and leads to the movement becoming a multinational insurgency. In the meantime, the weak economy has turned into a regional economic crisis that's spread to the Gulf Cooperation Council states.
This goes on for a while, but doesn't hit the top of the International Community's agenda until the regional crisis turns into a global recession in 2035 and violence spreads into Turkey, now an EU member, in 2036. The EU, which had been pushing for UN Peacekeepers to be deployed for several years, starts make much more noise about it. Mideast governments say no at first, but after suffering some serious defeats and attacks in 2037, Lebanon and Jordan agree to let EU military forces in (Syria, meanwhile, had already accepted assistance from Iran). Iraq refused outside help.
Ireland hosts an unsuccessful peace summit in 2039, followed by a more productive meeting in Dubai in 2041. A deal was finally reached at a third conference in Qatar in 2045, with insurgent/militia leaders agreeing to a ceasefire and a roadmap toward a power-sharing agreement. There's sporadic violence after that until sometime in the 2060s, when it finally peters out (largely due to the Spectro Generation nearing retirement age).
How is the Middle East looking as the world drifts away from oil?
As of 2080, not particularly good. Peak Oil, the recessions, the Depression, and the collapse of the Khaleeji really hurts the region. Governments, especially those who moved away from the EU after the Arab League went defunct, are short of cash and high in debt. There's been fighting between Sudan and Southern Sudan (a dictatorship) over remaining oil supplies, Somalia has turned totalitarian, and there's been fighting over access to fresh water in Iraq. Iran is fine due to having allied up with India a long time ago, and though the GCC hasn't been disbanded most of its members are falling into India's sphere.