I think it is a sign that you think everybody else is small minded that they might be offended by showing a sign of the culture in which you take part. Celebrate the differences rather than hide them, give people chances to learn rather than to hide and give more reason to separate.
Assuming people are bigoted enough to be offended by your well-wishes is very small-minded, IMO.
Isn't this what the US is all about? A way that we all live together, celebrate our own cultures and religions, and allow others to celbrate theirs?
I would hope that the Jewish person would have no fear in saying Happy Hannukah, or in accepting a hearty Merry Christmas, as we each wish the other our own cultural well-wishes and we, instead of hiding, learn about each other. This is the gift and promise of this Nation, that learning from each other we can move forward together rather than teaching each to separate and to hide our cultures from others. To be ashamed of expressing it, to "fear" other cultures and the thought that somebody might be offended rather than learn, this is never what the US is about, it holds no promise for the future, it separates rather than teaches, it is cold, and it is culturally bereft.