That is would be extremely strange. But considering I just said said it and nobody did anything (except for my boys giving me looks), this also fails a reality check.
It is true that some private organizations tell their employees not to say Merry Christmas on the job. But that isn’t the same as not being able to say it, just as me not being able to sleep when I’m supposed to be working doesn’t mean I can’t sleep.
h/t @Leslie Sowell
Edit: Susan Fred Schmerling pointed out that it is only saying Merry Christmas to the buying public while the employees are representing the company.
Edit #2: Dawn Geisler pointed out that “Christian nation” could mean a nation with an established Christian church. This obviously isn’t true of the US. However, I consider that to be a definition for a “Christian government”, with “nation” being what people who are members of that nation choose to do.