I have a lot of happy childhood memories of Christmas. As soon as I was old enough, it became my job to decorate the tree. I enjoyed the annual ritual of putting on a LP of Christmas carols, assembling the tree (we had an artifical one), unpacking all the baubles and lights and hanging them just so, for the best effect. My family of origin was agnostic, and the Nativity was just one cute story among several that marked the season -- the Saint Nicholas myth, Night Before Christmas, Dickens' A Christmas Carol (which as I recall, fails to mention Jesus much if at all), Rudolph the Red-nosed Reindeer (in a televised model animation), the silly TV announcements on Christmas Eve that NORAD radars had detected Santa on his way. In those years when it was our turn to host the annual Christmas dinner for my parents' circle of friends, I got to decorate the rec room -- I recall hanging one large banner reading "Season's Greetings". Apparently, the War On Christmas goes back as far as the mid-1960s.
During my Christian period, these secular syncretisms on the whole neither added to nor detracted from my observance of the Nativity. I simply ignored the parts I didn't like (Santa Claus, for instance: far removed from his origins as patron of the poor, now transmogrified into some shopping mall deity of conspicuous consumption). On the whole, I've always been pretty good at ignoring stuff I find personally irrelevant, while being happy to allow others to enjoy it as they please.
So really, I couldn't care less what the Costco greeter (I avoid Walmart) says when I walk in the door. "Happy Holidays"; "Merry Christmas"; "Salubrious Solstice" -- it's all good as far as I'm concerned. I find labels mostly arbitrary, so I really don't care what we call this year-end excuse for eating and drinking too much, and giving a few (hopefully non-extravagant, non-tacky, and non-useless) gifts to people you care about. I don't mind calling it Christmas any more than most (Anglophone) Christians seem to mind having their other major festival named for an ancient fertility goddess. As far as I could tell, the "War On Christmas" was an invention of a few (mostly American) professional blowhards, looking for an excuse to whine about how persecuted they are.
However, I suppose I can imagine someone who explicitly does not celebrate Christmas (say, because it's not part of their ancestral culture) getting a little tired of smiling graciously while being given good wishes in the name of someone else's festival. The obvious case in point would be Jews, who have a history some 17 centuries long of trying to maintain their separate identity on the margins of an overwhelmingly Christian society. What to my secular (though ancestrally Christian) self is a greeting with no deep significance could be taken as an affront. Which brings us, as it happens, to the real origins of the "War On Christmas", as reported recently at the Daily Beast.
Apparently, it really is all about the Jews. Who knew?