To me, Christmas is Christmas, and I like to wish people a 'Happy Christmas' in my cards. I wouldn't send a traditional Christmas card to someone of a different religion, but maybe a simple 'winter greetings' card if I felt it appropriate, so I guess they do have their uses.
Many years ago we lived in a Muslim country and we received an actual Christmas card and gift from our Muslim neighbours, which we thought was very nice of them. We reciprocated when they invited us into their home during one of their religious celebrations.
I think it's nice that there are appropriate cards we can give to others who don't celebrate Christmas as the religious holiday, but still may enjoy the 'Holiday Season'. When I was working, I had colleagues and acquaintances who were Muslim, Hindu, Sikh, Jewish, and we always made a point of having a little celebration for each others important festivals/celebrations. As someone else said, just go with the flow!