I'm trying to think whether I ever shook hands with any colleagues in the course of my work, and I honestly can't say I ever did. Not generally anyway - not part of my culture, or that of my colleahges, so far as I could see.

As for preferring to ask questions of people of the same sex, that sees pretty common too, where strangers are concerned, for example in in shops.

I'd suspect that's what invoved here is more culture than religion, though of course the two overlap. If you say "it's against my religion" that is quite a good way of getting people to back off from trying to get you to change your ways.