turncoat: [16] A turncoat is someone who abandons or betrays a group or cause and joins its opponents. The story goes – probably apocryphally – that there was once a Duke of Saxony whose territories abutted those of France. Clearly anxious always to make the right impression, he had a coat made which was blue on one side and white on the other. When he wished to be seen to be supporting the French interest he wore it with the white side outwards, and when he did not, he wore it with the blue side outwards.
Documentation of this tale is lacking, and probably the expression had a much less specific origin (the phrase turn one’s coat for ‘betray one’s loyalties’ is contemporaneous). [turncoat etymology, turncoat origin, 英语词源]
1550s, from turn (v.) + coat (n.). The image is of one who attempts to hide the badge of his party or leader. The expression to turn one's coat "change principles or party" is recorded from 1560s.