Privacy and Commercial Transactions
At some point during a commercial transaction, one often has to provide details such as where to ship the the goods, a valid email address to receive codes, etc. when shopping online. It does not matter how one pays for it, these details are necessary for the vendor to consummate the transaction. By their very nature commercial transactions require some loss of absolute privacy.
The only type transaction that is might have some guarantee not give away privacy is a cash transaction while picking up the product. Even here, store surveillance cameras will record you at the register and often will provide some details of what was purchased. The only difficulty is whether whether one can be readily identified by the cameras.