If they make it accessible enough, all stores may. Even if they don't, I imagine all stores will have something similar in some timeframe. So.. what will you do then?
I think that's unlikely. There is likely to be a large enough percentage of shoppers who avoid this sort of thing to support at least a couple of stores who make it a selling point that they don't do this.
But, if there is no option then I'll have to figure out what my response will be. It would likely have to be a compromise position between buying as much as I can without involving a store at all (buy produce directly from farmers, do a lot more bartering with neighbors, etc.) and employing single-use credit cards when I can't avoid the store.
That would be OK, actually -- there are still plenty of stores that don't use loyalty cards.
The difference between the two things, though, are that you can shop at a store that has loyalty cards without having to use them yourself. You couldn't shop at a store that uses this program without using the program yourself.