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POD: 840s. Emperor Wuzong of the Tangstays away from the mercury and, while no less devoted to Taoism & Confucianism, is less... thorough... in his efforts to clear out things he regarded un-Chinese heresies. Monasteries Buddhist, Christian, and Zoroastrian alike are still crushed due to drawing people away from their families and economic activity; but no efforts are made to prevent lay preaching while foreign ex-monks/nuns who were willing to do some manner of temporal/secular work and marry were permitted to remain.
In short, there develops a Christian (and Zoroastrian/Parsee) Hui analog in China. Largely assimilated culturally and almost indistinguishable by blood, following a generally 'low church' version of Nestorian Christianity, and in intermittent contact with the Middle Eastern Episcopacy.
Presuming many dead butterflies, how to the Jesuit and Franciscan missions that follow the establishment of a sea route from Latin Europe to the Far East react?