The point is being missed here.
OP is upset (although she says she doesn't care, but apparently she does) that checkout people are required to say Happy Holidays instead of Merry Christmas. SHE wants to be told Merry Christmas. Personally, I would tell her something else, but that's beside the point.
She indicated that she worked retail in the past? And wanted to tell people Merry Christmas instead of the more inclusive and professional Happy Holidays. Several of us explained to her that she doesn't get to make that decision when she's on the job - she should do what her employer asks.
Cashiers shouldn't have to ask your religion before they greet you. Happy Holidays shouldn't offend you, unless you're a kook.
No one is telling you not to wish people Merry Christmas in your personal life. And if you say Merry Christmas in your personal life, and someone gets offended, that is their problem and not yours.
So, to sum it all up, if your employer wants you to greet your customers with Happy Holidays, that is what you should greet them with and shut up about it. Very similar to if your employer wants you to answer the phone with, "Thank you for calling Super Sub 13th and E, this is Vraiblonde, how may I help you?" THAT is how you answer the phone. Not, "Yeah, whaddaya want?" or "Hello?" You have a script, the end.
The other issue is the overreacting zealots who get offended by someone saying Happy Holidays to them instead of Merry Christmas. And they can piss up a rope because if I wished someone Happy Holidays and they had a fit, my only other greeting to them would be "DIAF".