Clearly this is a YMMV issue. There are about a dozen Publixes (Publices?) in and around my city and I've tried about half of them. At one store in particular, on two separate occasions the cashier (different cashiers) asked to see the card and then showed it to the manager. Both times, I was allowed to complete the transaction and nothing else was said. That is my go-to store now, of course, but there is one other store that I also visit frequently. Never been asked for ID at any store, even when doing 2 x $500.

Almost everything I've used at Publix has autodrained; the only exceptions were a OneVanilla MC and a Vanilla VGC, both purchased at Sam's Club. OneVanilla Visa cards from CVS and gas stations will autodrain. Grocery Everywhere and Dining Everywhere cards will work at Publix; Style Everywhere did not work.