No, i am not a Rabbi but tefilla is an avoda sheb’lev and i cant imagine why as long as your dressed in a normal fashion (no pun intended) and your wearing a head covering of some sort, G-d wouldn’t want to hear from you as is, and if the purpose of the hat is for extra awareness of His being over you, well whats the davening for then? I understand for the amud maybe but just to daven…?!?!
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