The Greats were not necessarily of Han ethnicity, but this is not a thread about ethnicity, but national citizenship.
North Beggar Hung 7 Gung, for example, was purely a Han Chinese, but technically speaking, based as he was in *northern* China, he would have been a citizen of the Jin Empire during LOCH and a citizen of the Mongol Empire during ROCH. East Heretic Wong Yerk See lived on Peach Blossom Island off the Chinese coast, but I wonder if he fell under Sung or Jin citizenship?
West Poison Au Yeung Fung's citizenship is even more interesting to consider. His Mt. White Camel was located in Turkestan, which was under Chinese authority during the Tang Dynasty, but during the Sung Dynasty, that territory was under either Turfan or Hsi-Hsia's control. Au Yeung Fung would have been a Turfan or Hsi-Hsia citizen during LOCH and a Mongol citizen during ROCH.