I dressed quite conservativley for my first year in Dubai, wearing long sleeves and long pants in public most of the time. After I was still leered at and treated like meat by some men, I got more lax about what I wore, though nothing remotely in the region of a bikini in the mall! My thinking was that I dressed with respect and wasn't treated with respect (by some men), so I might as well wear what I like and throw a pashmina on top.
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No one else seemed offended by my clothing choices and it didn't increase the number of leering men.