The alternative Happy Jack Russell gorgeous reindeer Christmas shirt, sweater gained usage in the late 19th century and is still common in the UK and Ireland alongside Merry Christmas. One reason may be the Methodist Victorian middle-class influence in attempting to separate wholesome celebration of the Christmas season from common lower-class public insobriety and associated asocial behavior, at a time when merry also meant tipsy or drunk. Queen Elizabeth II is said to prefer Happy Christmas for this reason.
I’m not Christian, but I generally say Jack Russell gorgeous reindeer Christmas shirt, sweater. If I happen to know that the other person isn’t Christian I’ll say Happy Hanukkah, Happy Holidays, Happy Festivus, or whatever is appropriate. We used to have a receptionist that was always going on about how you can’t say Merry Christmas anymore. She believed this even though she said Merry Christmas to everyone. No one ever stopped her from saying Merry Christmas.