> It is that the Chinese religion, on the level of the popular practice and belief has these currents being practically inseparable from each other
The state itself drew lines separating these faiths. It is on the level of the people, who in practice syncretize their beliefs, that a unified image can be drawn. But in the history of the state, those lines were drawn by every dynasty in the history of the region. It is a question of where those lines are drawn.
> I myself raised and have labelled as a religion that really was not part of the Sinic worldview but was a foreign import
China is not unique in the practice of localizing religions. This is what occurred when the Greeks arrived in Afghanistan; when the Romans arrived in Greece; when the Greeks arrived in Egypt; when the Nords arrived in Russia; when Buddhism arrived in China; and further, when Confucianism, and when Buddhism, arrived in Japan.
> Your idea to represent Confucianism and Daoism with Pops is ultimately inaccurate and just leads to arbitrary lines being drawn everywhere.
I think rather than disagreeing about the actual nature of what occured, we may not be agreeing over what syncretization is. It is the process of religions being localized, the process of beliefs being harmonized, the process of cultural views and beliefs that at one point were different, becoming difficult to disentangle. A pop that is both Buddhist and Daoist is a way to represent the reality that over the long history of China, many governments in its history have- whether you may wish to draw those lines or not- drawn lines between those related beliefs, and chosen to impose sanctions, restrictions, or state elevations of some aspects of belief over others.
> These are primarily attacks and suppressions of an organised clergy and a current of thought that are trying to destroy it and weaken it. They are not institutionalised campaigns like the Inquisition trying to ensure that a population follows the correct orthodox religion
Suppression of some beliefs and ways of practice and not others by the state is something that is, quite frankly, more important to represent than whether or not those sets of beliefs are commonly held by the same people. The distinction of whether not not this falls under a Christian model of 'correcting' heresies is less important than the reality that beliefs were being suppressed. It does a disservice to the history of religion and practice in China to simply represent these beliefs which the state did not treat the same, as being the same.
This is why I suggested allowing the government to suppress or elevate beliefs, independent of whether those beliefs are the 'state religion'. It's not necessary to represent the Chinese state sending missionaries to enforce a code of state orthodoxy (although the Ming dynasty did, in fact, do something very similar to this in its enforcement of neo-confucianism at the level of temples). It would, however, be a good idea to represent the state cherry-picking beliefs they prefer, and elevating or suppressing them, as happened in history under nearly every dynasty in the history of China.
> even campaigns as extreme as those in Joseon Dynasty against Buddhism helped in crushing monasteries and monastic tradition but did not actually attempt to kick out Buddhism from society
Indeed, rather than remove beliefs, governments in China have historically preferred to officiate beliefs. Rather than 'remove' Daoism, the Ming dynasty sought to adjust Daoism to better conform to a more state-sanction set of neo-confuscist views. This was the common practice by many dynasties. Representing this would be highly difficult, and I agree that it would be nice to have represented. Other states with centralized state control over religion, such as Rome, or pre-Islam Egypt, frequently went through similar processes, adjusting state policy on different aspects of the beliefs of the various groups and practices within the Roman empire. Unfortunately, by the timespan of EU5, China and its sinocized neighbours are only states left that still had this level of state influence over the religions within their borders, and that makes it very hard to represent, since it's a method of organizing religion that's only possible insofar as there are little to no extranational authorities that dictate religious policy.
Imagine, for instance, if in medieval France the government picked some aspects of Catholicism, like Monasticism, and decided to aggressively suppress it. If France was the only Catholic nation, then we would describe this as a 'change in Catholic practice'. But because Catholicism is beyond just France, it would result in the Catholic Church declaring the French government to be heretics. Whether this results in an actual religious schism, or a temporary conflict, would have to be decided by history, and it would also be greatly complicated by the question of to what degree priests within France chose to actually do as the state said, or chose to remain loyal to the Holy See.
China doesn't have that concern. When a dynasty says, 'Alright, these practices are now a part of Confucianism, and these are not', then that's simply what Confucianism is now. How much the state tolerates deviations from that among regional parts of China depends largely on the dynasty in question, many of which were fairly lax, and some of which were very strict. I cannot think of a good way to represent the reality of the 'official' set of Chinese beliefs being shifted with different governments, particularly since, just like in Rome or Egypt, the government is in turn being shifted by changes in the views of the public over time as well.
I also do not know how to represent the ability of the state to change the views and practices of targeted groups within it either. In EU4, this is the premise behind Confucianism being represented with a 'Harmonisation' mechanic- representing the Ming dynasty's policy of deliberately syncretizing Buddhism, Daoism, and Confucianism into neo-confucianism. I don't like this mechanic, because it implies that if China somehow conquered Southeast Asia, then the Buddhists there would be fine with it, wheras the reality was that Buddhism in China was not the same as Buddhism in Southeast Asia, and Southeast Asian Buddhism would likely not be tolerated in the Ming Dynasty.
Valid concerns.
> These included not only the study of Daoism and Buddhism but the use of spirit-writing séances and prayers to Wenchang
This is syncretism. This is the adoption of practices from different sets of beliefs and ways, by others who otherwise would have a distinct set of beliefs. Not all within China practiced Daoism, and venerated the Buddha, and prayed to their ancestors, and held séances. Different groups and people held different sets of these beliefs, and the tolerance of these beliefs changed with the governments.
> an inseparable relation
You may think this of the people, but the governments sure didn't. And again, I would say that it's extremely important to represent the reality of state policy over the period.