Again" variants have proven quite popular.
One political party named after these objects opposed the Reduction Parliament during their country's Age of Liberty. A group of Turkic tribesmen named for their distinctive red type of these objects helped install Ismail I as the first Safavid Shah (*)   .  James Monroe was given a nickname referencing a type of these objects due to his role as the last major political figure from the American-Revolution era. A variety of these objects emblazoned with a political slogan has attracted controversy for being made in China. For ten points, name this type of object, whose tricorn and "Make America Great Again" variants have proven quite popular.
One political party named after these objects opposed the Reduction Parliament during their country's Age of Liberty.
Hats (prompt on "heads", "hair", and things of that nature before power)