Probably not on the basis that I avoid shopping if possible. Could be fun to try, though. Local laws demand underwear be worn when trying on clothing which is probably already honoured in the breach but it would then be more obvious!
Gaslight Records in Melbourne used to have an occasional nude day when they were in business. That could have been more my scene but for the trudge into their city location (i.e.: downtown) and that at the time I wasn't a nudist as such.
As a strict hypothetical nope I would not so shopping nude I a place not designated as such. If I lived in a society or community like Colina da Sol where that was the norm of course. However being fixated on going naked in public places where nakedness is not the norm is not part of my naturist way of life.
SunnysideSteve mentioned about a record store in Melbourne that had a nude shopping day.
I wonder if that was a thing for record stores to do.
I do not remember when this was, probably late 70's, when I saw a TV news story about a record store in Santa Barbara that had an annual sale for all that came in nude. They even had video of the event, naturally carefully edited. The store was located close to the collage there and the majority of the customers were obviously students.
The remarkable thing was the way the story was reported. They covered it like any news story without all the side comments you get today.
I recall another print story about a clothing store that had a promotion where they offered a suit with shirt, shoes, socks and underwear to the first person to come in completely nude.
Not sure what they expected but someone came in the first day of the offer.
In answer to the question, even under the conditions set, yes I would go shopping, or any other activity, nude.
I would. I go shopping practically naked anyway, barefoot in short cutoffs, commando and if I can get away with it shirtless but that's usually the reason to get asked to cover up even at the WalMart. I've gotten away with wearing a cropped mesh dago T in several stores so far and nobody has said anything about me being barefoot, so if all I've got on is a few ounces and lineal inches of fabric I might as well shop naked.
My wife and I have both shopped while nude, many times! Granted, it took place at the Le' Boutique at Club Orient but also, back when it was common, we'd walk down Orient Beach naked and shop at Sexy Fruits, Adam and Eve and the gift shop at the Old Kakao Bar and Grill.
As far as shopping naked presently, probably won't happen. Closest we've seen anyone close to nude is the supermarket near our club. There are a few women from the club we've seen at the market in sarongs. When they were walking, their sarong would open slightly, and it was no secret they were nude under the wrap. Evidently, the market management contacted the club manager and asked him to ask the residents and members to please dress appropriately when visiting the store.
This really pisses me off, especially nowadays. You can bring your dog into just about any store, but you're scrutinized for what you're wearing even if you're covered. By the way, I hate that people can't go anywhere without their dogs, and I'm a huge dog lover!