The biggest impact was undoubtedly in the effects in Palestine, at the end of the Ottoman Empire's life. After WW1, the region was conquered by the British, who governed the region with competing promised to both Jews and Arabs, formally kicking off decades of conflict.

This change in the geopolitical environment radically altered the climate of Zionist action during the period. During the Ottoman period, Zionist enterprises were focused on purchasing and settling land and creating an infastructure, to establish a permanent Jewish national prescence. But when the British were there, the door was opened to actual statehood. This is when you start to really get the proto-state organs that are a key feature of the situation in Mandatory Palestine under British rule--the Jewish Agency acts as a proto-government, you get paramilitaries starting in the 20s, you get the Histadrut (umbrella labor union), you get bus companies, etc.

There were also significant Jewish communities in the Balkans during this period, formed mostly of refugees from Spain during the Inquisition, but also a much older community in Greece. While I don't know of any effects of this specific to their non-Jewish neighbors, it's worth mentioning.