Well, you're Chinese so will clearly be better informed and your suggestion would carry more weight than mine. But just some points to consider
- From what I understood, the article explains that Shendao was at some point used to refer to Taoism and later on separated as a category of its own to refer to folk religion.
- I don't see a problem with using both Shendao and Shinto, especially if the game is in English - the words have the same origin but refer to different things. I see how that would be a problem in Chinese where you'd have the exactly the same words though.
- Finally, just to note that if Wu refers to shamanism, no other civ has Shamanism as their folk religion (even though shamanism was ubiquitous). There's generally a difference between shamanism and religion in that the latter is more organized and formalized in specific rituals or texts, and other details that might not be worth getting in to here. Instead all civs have the earliest religions that occurred after shamanism.
But all that being said and considered, I don't mind so much if the name is changed.