As noachides we are not permitted to wear anything that would cause someone to mistake us as a Jew like tallis, tzitzis, or kippot. As a Noachide when we attend the local 'Temple' which is unaffiliated with any sect, I should not wear a kippah as it may cause someone to mistake me for being Jewish. I just wear normal clothing (modest) as does my wife but how should I cover my head in shuls?
One source says in Noachides should wear a headcovering that s different such as a turban maybe or an Islamic style kufi. I am no good at turbans and I really would not like to wear a kufi if at all possible and be mistaken for a Muslim. What is something practical I can wear? Am I allowed a modest style hat in shuls? Or does it need to be a particular style of hat to be 'halachic' for noachides?