Keeping Your Scarf On in Church
Al-Hannah sells a pretty lacy al-amirah hijab that I think an Orthodox Christian could reasonably use as a headcovering. My thought is that a non-Muslim woman might wear the larger part of the covering on the back of the head, rather than surrounding the face.
How would this work? The front section, the part on the forehead, is completely separate from the larger covering section. You put it on first — around your head, above the eyebrows and ears — and it helps to keep whatever you put on second from slipping off your head. After you have this first part around your head, you could eschew the larger part altogether and tie a regular scarf on in whatever way you usually prefer. Or you could use the longer tube thing, the second part of the al-amira headcovering, as a back-of-the head scarf.
(photo credit to Josh Parrish)