I'm sure none of those cultures thought that before Islam was introduced
or does Christianity have a civilizing effect on the savages?
Quite frequently it does. See Imperial China. After missionaries started spreading Christianity in the 19th century, it was the Christians that rose against and tried to stamp out things like foot-binding, concubinage, polygamy and slavery. Or see Sati in India. It wasn't the Christians practicing that. Or barbaric human sacrifices practiced by European pagans that went away after conversion to Christianity.
Ummm... LOL? Christians having influence in China? What kind of drugs are you on tonight?