Recently we went to dinner at a hotel restaurant in Muscat. It was one of the higher end hotels, and the restaurant served wine, so I guess you could identify it as a cosmopolitan or liberal space. (As I understand it, few independent restaurants, and not even all hotel restaurants, are licensed, even in the capital.) The diners were a mix of Omanis, Europeans, and folks from other Gulf states (at least one man wore what I think of as a Saudi ghutra.)
Next to us sat a middle-aged Omani couple. He was wearing the traditional Omani cap and dishdasha. She was wearing a black abaya and head covering. After they ordered dinner, she removed her head covering, kissed her husband, and excused herself. She returned without her abaya, wearing a red tank top and jeans.
Both in Oman and in other countries, I have seen women and men in widely varying interpretations of modest dress. But I have not seen someone change their level of dress “in public”, if you will.