One size fits all policies--whether they be zero tolerance policies, mandatory minimum sentences, political correctness, or the equally inane fight against all political correctness--refuse to accept that most human beings have common sense. A six-year-old bringing a firearm to school is not equal to that same kid holding his thumb and forefinger in the shape of a gun. Some language is legitimately offensive--even if it isn't intended to be, or didn't used to be considered offensive--while other language really just isn't.
Someone wishing you a Merry Christmas is seldom if ever a slight against you or your faith, whatever it may be. Someone wishing you "Happy Holidays!" isn't, either. When stores make a policy that excludes either or only acknowledges one set of beliefs, they're not allowing good old common sense to rule the day. There is nothing wrong with hoping every customer enjoys all the holidays, including the ones they don't personally celebrate. And there's nothing wrong with offering holiday wishes based on the cues people offer, either. (A lot of times, you can figure out who celebrates what holiday based on clothing or other attributes.) Demanding that stores use any one particular kind of greetings and signage--whether all "Christmas" or all "Holiday"--is just questioning common sense.
I suspect that many believe in this "War on Christmas" nonsense because Christmas has been the dominant holiday for so long. Jews and others were just supposed to accept that numbers dictated that stores would have Christmas signage and offer Christmas greetings, and towns would have Christmas tree lightings and Christmas fairs. If those who didn't celebrate Christmas were lucky, there'd be some small recognition of their faith tucked in a corner somewhere out of the way...maybe. That some cities and towns, multi-state or multi-national chains and individual mom N pop stores have chosen to be more inclusive threatens those who want Christmas to remain at the top of the ladder. Every acknowledgement of those who don't celebrate Christmas is one less acknowledgement of the Christian faith. They call it tradition...but refusing to recognize that other faiths exist and deserve to be in the public square too is a bad tradition.
If it were up to me, we, the people would acknowledge and celebrate all sacred and secular holidays in the public square. Schools would teach about all religions, and children would learn the ethnic and religious traditions of everyone in their classes, their schools, their neighborhoods, and ultimately, the world.
I understand why this isn't possible--it's largely the same reason there is both political correctness AND the so-called "war on Christmas" &/or "the Christian faith." (For my money, the "War on Christmas" is just political correctness, Christian edition. Another interest group demanding that everyone give them the respect they think they deserve by virtue of the fact they exist. YMMV...) No matter how much we tried, some group--& more than likely every group--would think they were getting the short end of the stick somehow, or believe that some other group isn't worthy of the same respect as their own. It's a damned shame, but it's something we'll probably never get past... ...so rather than learning about and honoring all of our traditions and faiths, we can't honor any of them in our secular public square... It doesn't stop the complaining, obviously, but it does lessen it...