‘Turn turk’ in the Renaissance meant to convert to Islam. The Turks were the Muslims that the English had the most contact with, through the Ottoman Empire.
Because of the entrenched association of peoples until recent times with religion, changing religion was broadly regarded as betraying one’s core principles, and being literally faithless, renegade. It is so used, metaphorically, in Shakespeare:
- [Hamlet, Hamlet to Horatio] if the rest of my fortunes turn Turk with me (if my fortune betrays me)
- [Much Ado About Nothing, Margaret to Beatrice] an you be not turned Turk, there’s no more sailing by the star. (Margaret alludes to the fact that Beatrice has fallen in love with Benedick, despite her protestations: as complete a change as someone converting to Islam)
Hence, surprisingly enough, an accurate definition in, of all places, Urban Dictionary: to turn turk:
Chambers’ Twentieth Century Dictionary adds: “to go to the bad: to become hopelessly obstinate”. The value judgement of Islam = bad is what you’d expect from a majority Christian culture; the obstinacy is surprising, unless it is the generic obstinacy of a renegade.