Er, Miss Manners answered the question I submitted:
"DEAR MISS MANNERS -- At this time of year, I try to be respectful of the diversity of the people I may meet by wishing them "happy holidays." I like to think this neither assumes what they may celebrate nor imposes upon them what I may celebrate, but still manages to convey my good wishes toward them.
However, I have recently begun to think this may not be entirely appropriate. After all, some people may not celebrate anything at all this time of year, and I would not want to inadvertently offend them. I also think it might be even more respectful to show some interest in offering more than just a generic farewell.
Do you think it would be appropriate to first ask, "Do you celebrate a particular holiday this time of year?" I could then tailor my farewell to their response, from "Merry Christmas," to "Happy Hannukah," to simply, "Have a lovely day." I want to find a balance between being festive and friendly without appearing unduly personal or rude.
GENTLE READER -- Please do not go around interrogating random people about their religious affiliations and practices. It is disrespectful of their privacy. Besides, the number you might offend would be considerably larger than the number offended by being wished a generalized or wrong holiday greeting.
Miss Manners is well aware that there are some who do take offense at any such wishes, specific or not, including "Have a lovely day." If you really want to protect yourself, you would be better off asking, "Are you the sort of person who makes an issue out of a simple expression of good will?"
But as that, too, would be an invasion of privacy, Miss Manners is afraid you will have to take your chances or wish everyone a happy winter."
I actually submitted that two years ago. Neat! :)