Why is this being down voted? Do readers of this board really think a woman chess player from Papua New Guinea would be allowed to participate in a chess tournament on American soil if she refuses to conform to the US cultural norm that requires a woman cover her upper body when outside the home?
Isn't that exactly the point? By your own choice of words it's clear it's not culturally acceptable in the US and Europe, (except for specially designated areas/specially designated times).
[1]: http://gotopless.org/topless-laws