I am going to say something that will offend many of the Christians on the board but it has to come off my chest.
The core question is the greeting or well wishes meant to be FOR the benefit of the person saying it or the person it is being said to. If purposely saying Merry Christmas is to show off your religion, then it doesnt mean anything to me except to show me that you are maybe pushy and self centered in your witnessing and your well wishes are simply a foil to push your religion. You dont care about wishing me well.
OTOH, if you know the other person shares your beliefs then it comes off as a benevolent thought.
Most times this kind of stuff means little and most people let it pass.
I will purposely say Merry Christmas to my Christian friend as that is what I hope for them. Because I really CARE about my non-Christian friends, I say Happy Holidays to acknowledge that my greeting is not generic and not about me.