The Ottomans had a Caliphate since forcing the last Arab Abbasid Caliph of Cairo into turning over the emblems of his authority and mantle to the Turkish Sultan-i-Rum of Constantinople. Many Bedouins immediately rejected this seizure of power and would rebel against the Ottomans from then on. The Arab Revolt was led by the Sharif of Makkah Hussein ibn Ali, who declared his own Caliphate, whose army was largely made up of these disaffected Bedouins and cooperated with the British to establish an ethnic-nation for the Arabian race. So you see, it was not religious authority that made the Arabs turn against the Ottomans, it was the desire for nationalism as had succeeded in Europe at nearly the same time. Unfortunately for them, the English and French proceeded to ignore the Sharif of Makkah's Sharifah Caliphate, and did nothing when it was overthrown by Ibn Saud - except that the British permitted his sons to become kings of Iraq and Jordan. One son tried to become the King of French Syria, and was defeated by the French regular army and French Syrian colonials.

So it was not Arabs & 'Christians' against the Ottomans, it was more analogous to Giuseppe's creation of Italy, only that they failed in their attempt and were divided into protectorates, which were given Mandates by the League of Nations in order to create the ex-Ottoman territories of British Mandatory Palestine, the French protectorates of Lebanon and Syria (which rejected any Arab executive), and the British Mandate of Transjordan and British Mandate of Iraq. The Sultan of Egypt had also been independent and cooperating with the British for a long time by then. The claim was that they in fact were protecting these states from Ottoman reconquest. Kuwait, the United Arab Emirates, Oman, and Aden were already British territories at this time, having displaced the Omani Empire and before them Portugese colonies on the Arabian mainland. It's also important to note that many Muslims had been serving and continue to serve in the British and French armies ever since the beginning of European colonization of Africa in the 1800s.

Sharifah Caliph's former Kingdom of Hejaz would receive a new king after being conquered by the Saudis of Nejd, who immediately defered to their Nejd home base as the true capital of what would become the Kingdom of Saudi Arabia. This is why the capital of Saudi Arabia is in Nejd, in central Arabia, not the Hejaz, which contains Makkah and Medina and which has far more religious significance and a more cosmopolitan culture (think Hashemite Kingdom of Jordan) in contrast to the Wahabists Bedouins of Nejd. The Hashemites would continue, and to this day continue to cooperate with British authorities in order to check the power of the Arab states which surround and threaten them with things like Republicanism, Socialism, and dominance by the Saudis. Later, the Saudi's own allies who aided them in this effort, the Ikhwan, would rebel against percieved pro-Britishness of Ibn Saud, and the Saudis were harsh in their beheadings of all rebellious leaders. This is why they continue to pursue alliances with Western countries today without any interference from either Hashemites or Wahabists.