Well, I think alot of how the Muslim world would be perceived depends on when exactly the POD is. Obviously, the earlier the better. Assuming a WW1 POD, there is still going to be an image of the sick man of Europe, and the run of disastrous wars to back it up. The 1878 and Selimiyan POD's would change this alot. People couldn't think of Islam as a Asian and African religion, as there would be significant Muslim lands within Europe itself.
Islam itself is likely to be more liberal. Salafi influence will be curtailed, as the Saudis will either be irrelevent or non-existant, and there will be less resentment amongst Muslims for things the west has done OTL (no Israel, less western military intervention). Hopefully this will mean that Islam is perceived as less aggressive and combative.
But nobody really cared about the Ottoman claim of Caliphate I am told after a time, if not right at start; maybe because those were turks,a clearly national state at first, so it kinda spoiled it in the eyes of arabs.. or something...
I was always under the impression that it wasn't due to the perception of the Ottoman empire and Caliphate as a Turkish entity, rather that it was perceived as weak and unworthy to defend after its many defeats.
I suppose the attitude from the West could largely come to depend on how the Ottomans treat their Christian minorities. If we're assuming the POD here is they remain neutral in the First World War, the question must be, how decent was treatment of the Greeks, Assyrians and Armenians in 1914? Was it improving, or getting worse, vis a vis the situation in, say, 1900? Like it or not, Western attitudes, will, I suspect, be greatly influenced by the experiences of those Ottoman subjects that Westerners feel they have the most in common with.
This is quite an important question. Historically, the different groups of Christians had different situations. The Greeks had a Greek state around, and were very important in the economic equation as they made up alot of the mercantile class (although there was a growing Muslim mercantile class). If the Ottomans were neutral in World War 1, the Greeks can expect to have alot of the laws that gave them preferential treatment overturned, as the Ottomans abolish the capitulations which hampered them in the 19th century.
The Armenians, meanwhile, had no national state of their own to look to, and made a majority in no significant part of the empire. If the Ottoman empire stayed neutral in World War 1, there is a good chance that Tsarist Russia would make it through, seeing as how the allies would be able to supply them through the Dardanelles, and they would have one less enemy to deal with. Indeed, I think it was Falkenhayen who said that the war would have been over by some time in 1916 if the Ottomans were neutral. So there is little chance of an Armenian state appearing there, for the time being at least. Though the Russians are likely to appeal to the Armenians on behalf of Orthodoxy, there will be nothing like the Armenian rebellion and deportations of OTL unless the Ottomans get involved in a major war.
The Assyrians, I know less about (if only Leo was here...). What I know is that they made only a small minority in northern Mesopotamia, so they are unlikely to seek nationhood, so long as they are smart. This should be enough to guarentee them good treatment.
A key thing to remember about the situation of all the Christians (and the Jews) is that they were guaranteed equality earlier on in the 19th century, so all they really have to hope for is the enforcement of the decree that guaranteed them this.
No one really asked for this one, but the situation of Jews in the middle east is also likely to be light-years better then today. Most of the anti-semitism in the middle east is inspired by the existance of Israel. With a surviving Ottoman empire, there will most likely not be an Israel, and thus, alot of what inspires modern day anti-semitism will be gone. Maybe the Ottoman empire in general may be a refuge for Jews escaping persecution in Europe, as it was in the 16th century.
