Are you seriously suggesting that they did so because the Turks were Muslim rather than that it was in their perceived national interests to do so? That would be absurd.
No, I’m not. But I’m noting that the British perceived that what was in their national interest was securing Islamic hegemony over East Asia. The British Empire has always countered the insecurity of being such a massive empire ruled by such tiny islands by sowing division, disaster and discord everywhere, so their hegemony couldn’t be countered. Go ahead and claim it’s smart politics, but it sure as HELL isn’t Christianity.