I wrote a perl script to automate signing up for and downloading the bar code image for my local grocer's discount card without actually giving any name or information. I just print out a new one every month or so.

New employees occasionally get confused by the lack of a name but it's never a problem. I pay in cash, of course.

All the loyalty programs here (California) will let you provide a phone number rather than carrying a card. You should be able to use e.g. 867-5309 if you're really looking for anonymity.

There are websites that will give you a phone number for this purpose, but really what you want is a number that other people at the same store use, not a number that other people somewhere else in the country use.

At the grocery store I go to, the cashiers typically ask if you have a loyalty-program card and if you don't, they offer to swipe their own so you can get the discount. I suspect that's not allowed by their employer, but I don't see much downside as a cash-paying customer.

I really wish those loyalty cards were actually tied to my credit card. I’m tired of having to type my phone number into the system each time I buy groceries (with the same credit card).

At a lot of stores, it's pretty easy to get those without filling in the information lol. Usually they'll just hand you a form with the cards attached and ask you to fill it in online.

I have several cards like that which are not tied to anything.

Not if they want to aggregate your data with a thousand other databases.

Also, people can sign up for those with an alias, or throw away the loyalty card and get a new one on a regular basis (e.g. right after redeeming your points).