I can honestly say that in my entire life I have never been offended by a "happy_________" or a "merry__________" no matter what has been in the blank. whatever the case it is merely an expression of good cheer and to find offense in that makes no sense to me.
Personally, I don't celebrate the season at all. The only date that really stands out to me is the winter solstice, so if I were to say happy or merry anything, it would be "happy solstice."
When people say one of these to me, I generally just repeat what they said back to them. It's like when people ask how you are, you respond with "fine, and how are you..." To me it is just basic and simple politeness. Really I suspect it is only the media that makes a big brouhaha about it.
For people in the public eye, I think "Happy Holidays" makes more sense. Not because of offending or not offending, but because it is simply more inclusive. The entire season is celebrated and enjoyed by people of many different faiths. There is no reason to exclude anyone from an expression of good cheer.