I would be concerned in a healthcare situation (as someone above said students refusing to touch other sexes). When mum died, she was in hospital and had doctors and nurses 'working' on her for a long long time. She had a DNR and everyone knew, but that is a other story. If I thought that any member of the team hesitated for one split second just because she was female, I would be very very upset.
If a woman or man fell over in the street, or a child was crying, why hesitate. It is a other human being.
Belief is belief, but a human being is a human being. Sex is something else. If we can't treat each other with respect - I think refusing a handshake is more about you (the shakee) feeling that it is a violation of you and your beliefs, than the shaker (not wanting to out them in a moral situation).
Try to remember, in church (CofE anyway) part of the service is to handshake/hug your brother/sister in Christ, and this is in no way sexual. It is demonstrating that we are all children of the same god, and should treat each others as we would our own brothers and sisters. I do get annoyed when people equate morals with culture or belief. I have heard stories about people of a variety of religions that would make your hair curl - and if I asked anyone to guess which religion/or none they were, you couldn't guess.
I try to live by the 'do as you would to others' code. Ok, it doesn't always work out that way, but I try to understand other peoples beliefs and would like them to try to understand me. I they don't, we'll thats them and I won't try to beat them over the head with it. Some people - an any/all religion - try to do this, but I don't believe that you can 'make' people agree with your beliefs.
Here end endeth the lesson for today, brothers and sisters. Sorry it's a bit rambling, just pondering life, death and the universe today (one of my parents anniversaries today, so it gets you thinking).