According to Wikipedia:
"Religious syncretism is the blending of two or more religious belief systems into a new system, or the incorporation into a religious tradition of beliefs from unrelated traditions. This can occur for many reasons, and the latter scenario happens quite commonly in areas where multiple religious traditions exist in proximity and function actively in a culture, or when a culture is conquered, and the conquerors bring their religious beliefs with them, but do not succeed in entirely eradicating the old beliefs or (especially) practices."
So to sum up, it's when religious beliefs of disparate origins are blended together; often in the form of one god worshipped by a traveling people joining the pantheon of deities known in the lands they travel through, or in the instance of two separate figures of worship being conflated together into a single being. The latter is what we're discussing here
If I was to give an example of such a thing myself, this could happen in the real world if two adjacent cultures came into contact and both have say a trickster deity in their cultural zeitgeist. Some people might decide that hey, maybe they're actually the same god and start to spread that idea. Years down the road you have trouble disentangling two or more original lines of folklore that were gradually sanded down to make them being the same entity make more sense. For example if Trickster Deity A has a habit of turning into a pig in the course of his mischief, while Trickster Deity B had an affinity for birds; the later Trickster Deity AB might be depicted as a winged boar.
The difference is that in the real world these are just stories, bits of mostly oral tradition that are passed down over generations, changing as they are told over and over again. In a setting where the gods in question have their own thoughts, memories, and personhood, I feel like the notion of intentionally attempting to shape the religious canon (which will in time reshape the god itself to match) takes on more of a sinister tilt.
Consequently, that actually makes sense to me as the sort of scheme that the ever-ambitious Kanako might come up with to deal with a stubborn native deity who has made herself indispensable to the continued prosperity of her lands. Best case scenario for her: either she or the mentioned husband incorporate the legends of taming the Mishaguji into their own folklore while the god of Moriya is forgotten. Evidently, that is not how that gambit played out.
All that being said even in Risui's version (of Zun's version) of events the only thing pointing to any of what I just said being even kinda relevant is that offhand "Get Syncretizin'" in one panel of a chapter that wasn't focusing on them. But it piques the curiosity nonetheless.
