I think it ends up being more nuanced than that, with plenty of gradations of all of those factors.

If it means, "Literally nobody can know whether I prefer pads or tampons, and where I get them, not even the person I buy pads or tampons from", then I'm going to lean toward paying cash at some random drug store. A brick and mortar because getting things shipped to me requires giving them identifying information, and cash because it has literally zero fees and leaves no paper trail.

If I have to buy something online, then I already have to give them my name and address so I can get it shipped to me. At that point I may not care if my bank and the credit card processing agency also have a record of the transaction, because the info's already out there. At that point it's just a question of whether there are privacy laws that prevent parties from selling too much information or not - either way, I'm guessing 1 and 3 parties will ultimately fall in roughly the same equivalence class, on the privacy front.

Personally, I don't see a middle path where blockchain is preferable to either of those options. If I want complete privacy, then I don't want that transaction appearing on the blockchain, either. If I don't, well, might as well get some consumer protection.