分久必合，合久必分
Chinese historiography sees China's periodic breakup and reconstitution as part of a cycle, where both changes are demanded by the times. The chaos of a decrepit state or the chaos of a country split into warring regions are both equally intolerable.
However, hard experience has also taught the Chinese that every one of these struggles cause the common people to suffer greatly and for millions to die (e.g. https://en.wikipedia.org/wiki/An_Lushan_Rebellion#Death_toll , although there's some debate here)
> Not saying Xiuquan was right but it seems their main crime, as with all failed revolts, was losing.
Yes, the crime was losing—if they had managed to overthrow the Qing and establish a stable state then they would be seen as possessing the 'Mandate of Heaven'. But if you're going to rebel, lose and take 30 million people with you, fatally weakening the Qing state in the process and setting it up for more colonization by the West and Japan—what was actually accomplished by this enormous cost of human suffering?
It's not religion per se that the state fears most, just any source of authority that can inspire the common people to rebel against it. Communism certainly worked well recently.
The West has had the fortune of recent history from the post-Renaissance era being a time of generally increasing standards of living and political liberation. From the French to the American to the Glorious Revolutions, they are seen as successful struggles against backwards tradition and monarchy.
China on the other hand has both the blessing and curse of remembering 2000+ years of both cycles of prosperity as well as collapse.