[The PLA itself is not a monolith, correct?]
No Chinese army is a monolith. Military commanders and influential courtiers have repeatedly taken or attempted to take the crown for themselves, either for the empire as a whole or for the parts that they governed when opportunity arose.
https://en.wikipedia.org/wiki/Zhao_Tuo
https://en.wikipedia.org/wiki/Cao_Cao
https://en.wikipedia.org/wiki/Sima_Yi
There’s a tendency to see the Chinese as a bunch of robots who just take orders. In reality, the show of obsequiousness is just that, a show. It’s not for nothing that Sun Yat-sen, the man to whom the collapse of the last de jure Chinese dynasty is credited, said that the Chinese were like a sheet of loose sand. By that, he meant that they looked to the interests of self, blood kin and clan first and foremost, whereas the state was an abstraction.
https://jme.bmj.com/content/31/3/159
[Two stories from Confucian Classics reveal that legal justice or retributive justice had no absolute power in Confucius’ and Mencius’ ethical theories that social justice might sometimes have to be compromised with or even be overruled by filial piety and family values. Firstly, it is recorded in the Confucian Analects: The Duke of She told Confucius, “In my country there is an upright man named Kung. When his father stole a sheep, he bore witness against him”. Confucius said, “The upright men in my community are different from this. The father conceals the misconduct of the son and the son conceals the misconduct of the father. Uprightness is to be found in this.”10 Secondly, it is described in Mencius: Tao Ying asked, saying, “Shun being sovereign, and Kao-yao chief minister of justice, if Ku-sau [Shun’s father] had murdered a man, what would have been done in the case?” Mencius said, “Kao-yao would simply have apprehended him”. “But would not Shun have forbidden such a thing?” “Indeed, how could Shun have forbidden it? Kao-yao had received the law from a proper source.” “In that case what would Shun have done?” “Shun would have regarded abandoning the kingdom as throwing away a worn-out sandal. He would privately have taken his father on his back, and retired into concealment, living somewhere along the seacoast. There he would have been all his life, cheerful and happy, forgetting the kingdom.”18]
It’s precisely because of this disrespect for authority at a fundamental level - the notion that legitimacy is merely a matter of prevailing in a power struggle, that makes Chinese rulers very cautious about their subordinates. The absolute power held by Chinese rulers equally makes their subordinates unsentimental about removing or killing their superiors. Which came first - the chicken or the egg? Whatever the answer to this question, the reality is that all Chinese rulers view their courtiers with a wary eye, and vice versa.
Within the party itself, Lin Biao, Mao’s right hand man for a time, was alleged to have mounted an abortive coup against him. https://en.wikipedia.org/wiki/Project_571 Similarly, Bo Xilai, the Party aristocrat who was arrested for alleged corruption years ago, was said to have been in the initial stages of mounting a coup. https://en.wikipedia.org/wiki/Bo_Xilai The most well-known coup is, of course, the one that succeeded, which removed Hua Guofeng from power in favor of Deng Xiaoping. https://en.wikipedia.org/wiki/Hua_Guofeng#Ousting_and_death
The divisions are, IMO, not so much a matter of ideology as a matter of individual ambition. But ideology will be seized upon as a rallying point, if only to give their supporters something other than “more of the same” on which to hang their hats.