USA never declared war on Turkey. The American Colony in Jerusalem was quite active in WWI especially with relief work and aid (esp Turkish hospitals). " A little America close to Jerusalem's Walls". Many of the photos of Gaza/Jerusalem from the Axis side were taken by Americans in the Colony. The Germans and Austrians wanted a stake in Jerusalem and had sizeable contingents there at the "request" of the Turks. The British Empire had large populations of Muslims in India (Pakistan, Bangla Desh now) they were not prepared to antagonise so a conquest was seen to be a liberation and then mandated territory and spheres of influence. France Britain and the Sykes Picot carve up.The idea of Jewish homeland makes for a complex mix and the USA certainly had a stake in that in the 1920s. Too much for here but the British in Iraq, Jordan and Palestine adopted a form of colonialism mostly to do with oil exploitation.