I don’t carry a cell phone, although I technically own one (it usually stays at home). For a while I had to tell a cashier that I don’t have a phone on occasion, but I’ve noticed that many places seem to be backing off on pushing their apps or requiring a phone for some part of the transaction.
I used to carry a legit dumbphone (not one of the new Android/AOSP “dumbphones”) and that worked just as well. It’s even trendy now!