According to the prepaid SIM card wiki, it is possible to get a SIM card as a foreigner in certain "flagship" stores:
The problem is recently, that most shops - even the small newsstands - only accept the machine-readable Chinese ID card. Foreign passports seem to be accepted only by the flagship stores of the providers (or at airports)
However, when I tried to buy a SIM card with data plan, they told me that they needed a Chinese ID Card (身份证), and it was not possible to register with a foreign passport. I tried 10-15 different phone stores in several major cities and they all refused.
Has anyone successfully registered a SIM card with a foreign passport recently, or is the wiki page out of date? If this is still possible, what are the "flagship" stores that do this?