When I lived in the USA, many places used to have signs "No shoes, no shirt, no service" a sentiment with which I actually agreed.
It's reasonable, IMO, to think that anyone walking down a city street is likely to want to visit a shop, store, restaurant or whatever at some point.
I tend to think it shows something unpleasant about the attitude of someone who does this and I personally tend to avoid them.
Having said that, on a beach road, my stance is "up to you" but it still says "something" about the person.
I personally feel uncomfortable going shirtless in the street but sometimes I walk the beach (say Pattaya Dolphin to Walking St) and I'll take my shirt off, but put it back on when i return to the street.
UPDATE - Cross-posted with @jippytum above