Ostensibly... But if you ever pay with a card, it's quite likely those with the data will be able to correlate your cash purchases with the card purchase and thus identify you.
It's not like your cash purchase of 58.32kr has a match 578.32 kr withdrawal; that cash was taken from an ATM in a large, round-number bundle.
If you ever misremember the amount cash in your wallet, and, rather than just abandoning your basket at the checkout when you discover this, you pay with a card just one time, for that exact basket, when there is no cash customer for that basket on that night, they can now be pretty certain about who customer #5678 is, and can then link you to 95% of your historic purchases too.
OpSec is hard, yo.
For example, store POS system tracks nearby MAC addresses (simplest to do, very archaic). You always have your phone on you. Game Over. Even if you pay cash, if you've ever paid with a bank card connected to your identity next to that phone a logical inference can be made that the cash transaction XYZ is related to pseudonymous ID ABC if phone P's identifier was present at time of purchase.
That's what the entire point of things like Google Wallet/Pay is. Another means of directly attaching payment methods to your ID. Once that bank card is connected to you all transactions for that card from any source is also connected to you. From that every ID present at time of purchase is one step removed from you.
And so it goes...