According to the Pew Research Poll, of the 18% of people that believe that Obama is Muslim, 60% got this information from the media.
If I were Michelle, I might not want to go to Saudi Arabia either. I've travelled on business to the UAE--a very Westernized Middle Eastern nation--and as a woman it was odd to say the least. I stood out like a sore thumb. They didn't know what to do with a woman. Bathrooms were a particular embarrassment, as one place didn't even have a woman's bathroom. Luckily (!) our conference room was bugged, and as my colleague and I were trying to figure out what I was going to do about the lack of a door on the (men's) toilet--he was trying not to laugh as he refused to guard the entrance--the British secretary came running down the hall and said, "Oh yes, when I first got here I said this would not do at all, not at all! Come with me, I had this toilet installed soon after arriving." In Egypt, the bathroom was a stall in the kitchen. Try taking a 35 hour trip then having to use a stall in the kitchen the next day at work with your work colleagues making coffee. Talk about embarrassing.
I tried to not stand out, dressed conservatively. And they let me do my job. In Saudi Arabia, they would not have let me do any kind of work. And I would have had to wear long dresses and head coverings and wouldn't be allowed to drive or go anywhere without my husband. Michelle may not travel to Saudi Arabia because she can't agree to those conditions. Not to mention the fact that it's very dangerous. They have their children to think about.