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What I have experienced first hand, and heard about second hand, was people who have been offended at the words "Happy Holidays", or who, when hearing the words "Merry Christmas" from a businessperson, went on a rant about they're sick of no one being able to say "Merry Christmas". My youngest son, a convenience store clerk, has several times this year been the recipient of verbal abuse for saying "Happy Holidays". A few years ago I fielded a call at my place of business from someone who was so happy that one of our holiday ads said "Merry Christmas", taking the opportunity to disparage anyone who said "Happy Holidays". When I worked for UPS I encountered something similar. So, in my own experience, even saying "Merry Christmas" triggers some of these people into an often abusive rant about people who say "Happy Holidays". One of the stupidest things I've seen online was a tweet by the big-haired recent college grad who's claim to fame was posing with a semi-automatic weapon on her campus. This morning she posted a video of herself saying "It's 'Merry Christmas', not 'Happy Holidays' PC libs" and shot up a sign that said "Happy Holidays". Aside from the weirdness of shooting up a handmade sign, the mindset that thinks that It's "Merry Christmas" as if there are no other midwinter holiday observances tells you all that you need to know.
No one, outside of a few nut-jobs is literally offended at the words "Merry Christmas", is offended that you are saying them to him or her, is trying to ban them from store ads, or to stop people from publicly celebrating Christmas. What some people are doing is insisting that the religious aspects of Christmas (and c'mon, if you don't realize that Christmas has had it's religious roots largely commercialized out of it over the last few generations isn't paying attention or is living in a "Christian Nation" fantasyland) be kept out of official government displays and observances and that retailers consider other groups and be inclusive by saying "Happy Holidays".
Christmas, while still a religious observance for Christians, has become a secular holiday, and has become filled with secular and pagan traditions that have nothing to do with the birth of Jesus. The secular traditions have swamped the traditions and observances of other cultures (Hanukkah is a great example - Jewish parents have long had to battle the influence of Christmas traditions overshadowing Hanukkah observances - it's not "The Jewish Christmas") and even minimized the Christian core in favor of gift-giving, trees and Santa Claus. If you're going to get righteously indignant, get worked up about that.