China is very much threatened by inter-ethnic and interfaith conflicts. That's why they've rounded up their Muslim inhabitants by the millions and put them in concentration camps and torture them under "re-education" programs. China is so centrally managed because the leadership is deathly afraid of anyone who doesn't swear absolute loyalty to the party.
Interethnic and sectarian conflicts can threaten any large country simply because of its size, and that is why central governments exist to deal with such issues. Another issue is that I don't have strong confidence that a few million inhabitants can so much threaten the integrity of a country with 1.4 billion people predominantly belonging to one ethnic group called "Han", which makes up 93% of the population. For modern China, ideological and property stratification is much more dangerous, when the political system may not keep up with the rapidly growing well-being of citizens who may demand more respect for their own opinions.
I think the fact that China has instituted such a controversial program belies this point. If China wasn't worried about the minority populations, there would be no need to put them in concentration camps and force torturous re-education programs on them. At the very least, it's threatens to turn the world against them. I think wealth stratification is another threat (related to what you said as ideological and property stratification) which is why the communist party is so obsessed with growing the Chinese economy at any cost, including controlling the media so no other narrative can be told other than the glowing success of the Chinese economic miracle, and the party delivering enough tangible benefits to make the however much of it that is illusory seem true to placate the population.