NJ writes:
Asking somebody what brand of toothpaste they use could probably be construed as none of anyone else's buisness either, but I wouldn't imagine it being a source of embarrassment.
Anyone asking that kind of question in my circle of friends would watch the person they were talking to slide away (as CK did above).
The thing is, you ask yourself, "what on earth did he/she say that for?" and look for that slightly glazed look in their eyes. Replace tooth paste with belief in a god and it becomes inapproriate in a social setting. It's just not done.
At my house warming I discovered that two of my girlfriends' friends where xians. Even when I brought the subject up (I was a little drunk and spoiling for a fight) they declined to enter into a discussion.
Private and personal you see.