It's most commonly known as the nickname of Monkey D. Luffy, the main protagonist of the popular manga and anime series "One Piece". This is because he wears a distinctive straw hat throughout the series, which is also a symbol of his ambition to become the Pirate King.
So, when you see "mugiwara" in the context of "One Piece", it's most likely referring to Luffy or his crew, the Straw Hat Pirates.