Before anyone gets too self righteous about the subject of political correctness in this instance. It is purely the end result of intolerant vitriol that was spread by Christian fundamentalists who wanted to supplant the current secular holiday with a religious holiday fully devoted to their God. Basically it was a attempt to hijack the holiday for use as a propaganda tool. It wasn't divisive prior to that point, but it has been ever since.
The problem is we have two very different holidays on the same day. One is a religious holiday, and one is a secular holiday, and one of those holidays is trying to eat the other one. Whether the celebrants of that holiday wanted it or not. Well they didn't, and they weren't going to tolerate someone trying to force them out of their holiday. So they decided to say they wanted a divorce.
Which of coarse puts companies on the spot. If they wish people a Merry Christmas they are siding with a religion against everyone who isn't of that faith. While wishing people a happy holiday is like saying we don't value any one group of people over any other. Which is pretty safe, because only a ass bitches about a generic well wishing. It hasn't mind you stopped a lot of those fundamentalist ministers from now bitching about people no longer using their name for the holiday.
Anyway it wasn't Atheists, Agnostics, or Non Christians who are the root culprits in all of this name changing. They weren't the ones who had issues with the name. Everyone was happy until someone tried to force a god on some people who weren't interested.
Personally I think well wishes shouldn't have added meanings, and it sucks that is the case now, because just a few assholes had to go out of their way to do just that. I usually wish people a happy holiday, because as sad as it is to say. I would rather not offend someone, or come across as making personal judgments. That isn't to say that I will not wish someone a Merry Christmas if they wish me it first, but I won't go out on that limb myself. Anyway give it fifty years, and nobody outside of a church will wish anyone else a Merry Christmas. They will just be the Holidays plural.