Not only in China among the Taoist/Han culture, there were also old monasteries in Mongolia, built in the early 18th century dedicated to Guan Gong, in areas such as Khovd, Zavkhan and Ulaanbaatar.
I personally think that which deity a lama promote is a matter of personal choice, most of the time due to affinity and there should
never be a restriction or ban towards a certain deity for reasons that are not understood even by scholars and masters who could debate the nature of emptiness or phenomena!
There are sources that indicate Sangharama as a Bodhisattva, but again, there are also many sources that indicate Dorje Shugden as an emanation of Manjushri Bodhisattva as written and spoken by High Lama, including His Holiness the 14th Dalai Lama himself. But why are they neglected now and the focus became the few issues (again, the reasons are not convincing nor logical) that might arise due to the "worship" of this protector?
If worship of unenlightened/mundane protectors bring about disaster, threat to His Holiness' life, and the causes of Tibet, then we should dethrone all
Jigten Chokyong (worldly protectors) in Tibet and all of them in Tibetan Buddhism. Remove all protector houses for
Gyel,
Se, and
Tsen in Tibet and India, starting of course with the most famous mundane dharmapala Nechung.