(Let me preface this by saying that I know nobody cares - and yet, this is what goes on inside my head.)
The other week, the boys and I were kicking soccer balls around outside the university library. (It had just rained, and this is the only place in town that is all of paved, low-mosquito, well-drained, and mostly flat.) A professor-looking fellow came out of the library and stopped to chat with my kids about soccer. Another dude I know stopped and said hi. The professor introduced himself; he is African and has a very Muslim/Arabic name (think Mahmoud).
So I didn't put out my hand to shake his when he introduced himself, because some religious Muslims (and Jews, for that matter) don't care to touch women to whom they aren't related or married. He, of course, put out his hand, because he's a university professor in a small town and that probably wouldn't go so well, so then I shook his hand, and then I wondered if I'd insulted him or if he even noticed or cared about any of this.
Dr. S worked in a lab full of devout-Muslim Turks at one point, and at another point I spent a lot of time in the Orthodox world, so I got used to not offering to shake hands with anyone who was male and obviously religious in any way. But that probably doesn't come up all that much around here, except maybe with Christian fundamentalists.
(It's a weird place inside my head sometimes.)