eh, that's just the syncretic character, like how buddhism also blends in with local pagan stuff everywhere
it's a consequence of universalism of abrahamic religions that you don't see that much elsewhere and we in the west thus also don't know how to detach it since christianity leaves very little vernacular rites (especially once you get into reformation branches)
consider then how varro writes about how religion can be split into three different aspects, that can coexist and blend together as they deal with completely separate matters: civil theology (state cults, today the state holidays would fall into this matter though few view them as religious), natural theology (concerning the nature of the divine – here is where the philosophical stuff happens), and mythical theology (bible study happens here, also all the mystical rites)
similarly there were three types of religious participation in hellenistic religion as well: state cults (initially dedications to local city-state's patron deity, later roman imperial cult) and ethnic religion pertaining to more every day matters, with plethora of minor deities invoked; philosophical religions such as neoplatonism; and various mystery cults (e.g. eleusinian mysteries)
it's unfortunate that you don't get to see non-chinese daoism I guess, so we find it hard to disentangle that