Years ago, long before 9/11, my mother and I took a Mediterranean cruise which started in Istanbul, Turkey. One of the sightseeing trips involved a tour of the former St. Sofia Greek Orthodox Church which, during the days of the Ottoman Empire, had been taken over by the Muslims and later became a museum. We ladies were advised to not wear sleeveless shirts and to take off our shoes before entering, but we were not required to cover our heads. My mother grumbled at taking off her shoes, but I said, we are guests in a strange land and in a strange culture and as good guests, we should as much as possible adhere to our hosts' customs, traditions and rules. I compared it to the days when the Catholic Church required women to cover their heads. A female visitor to a Catholic Church back then would be expected to cover her head. Why should we not follow the customs of another faith when we visit that house of worship?
By the way -- dang shame the radical Muslims have made touring Istanbul and other parts of Turkey dangerous or I would highly recommend visiting St. Sofia. it's an architectural and engineering marvel.