I understand that in historiography counterfactuals are of limited use and I'm also aware that as a medievalist I'm far from the perfect person to be writing this op, but I thought this might still be an interesting question to put forward.
Had the Ottoman Empire not entered the war in 1914 (and I understand this would have been detrimental to their co-operation treaty with the German Empire), the situation in Palestine could have been radically different, due to the lack of the need for a LoN Mandate and no one to enforce the demand for a Jewish Homeland in Palestine. True, there was Zionist settlement in Palestine prior to this and of course British areas of influence within the Empire, but it would have been unlikely to gain as much traction, given the Ottomans would have given priority to any Arab/Muslim majority.
Of course, technically the Ottoman Empire was a caliphate, the Kaysar i Rum had caliphal authority meaning all Sunni Muslims owed it deference. Rather than being a radicalising force, it could be a moderating one. The Caliph issued many binding edicts which attempted to moderate Islam such as attempting to outlaw slavery or no longer making apostasy a capital offence. Some of this had quite limited effect, but the unifying element of the Caliphate could have be considered preferable to the modern state of affairs where every scholar with a tv show can proffer his own version of Islam.
This is one of the reasons why the the Ottoman Empire as a bulwark of traditional would have stalled the growth of radical Salafism. The other more significant reason was because the Ottoman Empire, and its Mameluke clients had frequently battled the Wahabbis of Nejd. It is highly unlikely that the Ottoman Empire would have brooked the growth of Ibn Saud in the Arabian Peninsula and even less likely they would have allowed the sanctuaries of Mecca and Medina, or even Hejaz as a whole, to fall under the control of the Wahhabist-backed Saudi Dynasty. Of course, it could be argued that given its failure to suppress the Hashemite rebellion, it would have had similar difficulty suppressing the one from Nejd, but one has to consider the impact of WWI on its ability to respond.
I certainly don't wish to paint the Ottoman Empire as some sort of utopia. It had strong tendencies towards massacre and we must not forget the Armenian Genocide, which cannot be attributed solely to WWII. The millet system still placed many minorities at the whim of the Sultan, though many were able to exploit it to their own benefit. The ideas of Ottomanism could have overcome these difficulties, but it's very difficult to speculate given the strength of the strongly Nationalistic "Young Turks". However, the Arab dictatorships and absolute monarchies that succeeded certainly didn't provide more security to minorities.
So, would anyone with a bit more knowledge on the subject wish to contribute? What did we lose and what did we gain through the collapse of the Ottoman Empire?