Out of a reflex of distrust, I refuse to participate in any kind of loyalty program of the outlet of the large retail store around the corner.
I tell myself that by refusing to join the loyalty program (which basically comes down to scanning an anonymous loyalty card every time I make a purchase), I prevent them from adding my correlations (what products I buy, in what combos, at what time) to their data.
But since I normally pay by card, I guess they can (and do) already do that with my bank account information?
If I would pay with cash, they can still see those correlations per purchase, but they can't track my purchases over time?
Depends on the store.
Your non chain store that has a loyalty program, probably doesn't have the interest or capital to pay some third party to manage the data collection and analysis to try to direct market things to you.
Worked at a co-op grocery store for a while. The "owners" could use their owner number to keep track of their purchases to count towards their patronage refund amount and it also allowed some limited ability to look at full transaction information to deal with misrings, returns without recipts, etc. in the decade that I worked there, there was no effort or interest (even though the people running the coop at the highest level were definitely "business goober" types) to try to use the info for direct marketing or to sell to a data broker.