While it is true that missionaries conflated “universal values” with “Western values,” that is not necessarily the case today. But the missionary legacy means that the Party can encode the creeping menace of Westernization with any belief system that makes claims to the universal. Global religions are scary not just because they fall outside the scope of Party power, but because universalism challenges fundamental ideas of political orthodoxy in China.
The emperors often had trouble understanding the universal pretensions of Christianity and Islam. It’s worth noting that the Qing emperors were often excellent at co-opting some of their subjects, whether Tibetan Buddhist or Chinese Confucian, but could never seem to grapple with the complexities of Islam and Christianity. In the case of Islam, this led to a cycle of rebellions and coercion. In the case of Christianity, proscription until the gunboats came and forced the Qing State into an accommodation which, rightfully given how it happened, still rankles to this day.