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There is a connection between Cai and Chiang through the Song sisters, but not one that brought Cai and Chiang together. Cai Yuanpei and Song Qingling both joined the Chinese League for the Protection of Human Rights 中國民權保障同盟 which criticized Chiang's repressive government. Cai was a witness at Chiang's wedding to Song Meiling, but you are right, the two were mostly at odds.