I was warned before going to Yemen that you have to be very careful about TWA (Travelling While American - and luckily I have dual American/Finnish citizenship) so I travelled as a Finn.

I have no idea what your motivation was for going there, but if I ever found myself in the nightmarish situation of being in one of those places, my answer would always be, "I am whatever you are." I've lurked in enough English speaking Islamic bulletin boards and chatrooms to know what these people are all really thinking...and saying out loud, when they don't realize that non-Muslims are within earshot. Or in the case of the internet, "eyeshot." These countries aren't like Utah, where the worst thing you could possibly expect to receive when people discover you aren't a Mormon is a "disapproving glance."