Maybe you could see Islam Nusantara for inspiration regarding the "worship" of traditional deity
Had that in mind actually. Basically, the more lower class Han converts (as opposed to literati conversion and Arab/Persian/Sogdian Muslim expansion through intermariage) you get, the more these practices will become prevalent, and the more the Imamate will have to find a formula to accomodate them, while delineating what is permissible and what profane.
Mind you, at some point you are also going to get a counter-reaction aiming to purge Chinese Islam of "local superstitions", especially if when performing the Haj to Mecca becomes a major thing.
Generally speaking, the spread of Islam within TTL China is similliar to that of Islam within OTL Java in that it is by persuassion and economic inducement (trade contacts) rather than coercion, conquest prestige or "hard" state power inducements, at least until a critical mass is reached. The difference is that the Shia in China will have a "pope" like figure who has the authority to make binding rulings on what is permissible, which makes it more adaptable in some respects, but more rigit in others. In addition, said pope figure will always keep one eye on his adherents in Central Asia, Persia and Messopotamia and will hence not wish to deviate too much. At most, he will permit accomodation and reinterpetation of local customs - but will not incorporate them as core beliefs.
So my models for accomodation, adaptation and evangelization are:
1. Islam Nusantara, as you said.
2. The spread of Manicheanism within China and Central Asia.
3. To some extent, the spread of Christianity within the Roman Empire/Post-Roman Europe, and it's eventual incorporation of pagan Gods into its collection of saints.
but....
3b. With the cult of Mithra being a somewhat more relevent example in terms of evangelization MO. Shia Islam will definately kick off in CHina as a "soldier's religion", and the mass of its early converts will be Turkic and Sogdian mercenaries/auxilaries rather than Han.
4. Various Zorastarian-gnostic-shiite fusions which occured throught the 9th-12 century in Persia and Central Asia (for one thing, variants thereof, will rise, be crushed, and flee to China)
5. OTL spread of Hui, but on steroids, with an earlier infusion of a seed of Middle Eastern and Central Asian adherents, and repeated later infusions, converting through intermarriage with Han women.
and...
6. The Bahai'i who are a late 19th century Shiite mutation.
That said, Confucius (and other competing Chinese traditions?) and Zoroaster will be recognized by the Imam as Divine Prophets *as they were by the Ahmadis) with relatively minor criticism of the distortion of their teachings by current followers. Perhaps Budha and even Lao-Tzi will be as well, albeit with
very heavy criticism of the distortion of their teachings. Mani will be denounced as a false, even Satanic/Aharimanic prophet.