I really don't mind "Merry Christmas." I know I celebrate Christmas, so, obviously I have a comfortability bias. But, I guess I think Christmas is a national holiday. Our nation, for better or for worse, was founded in Christianity. It's American culture to say "Merry Christmas" around December 25th.
"Merry Christmas" is not (and should not be) mandated American culture by any means. People who are offended by "Happy Holidays" can choke on a candy cane. Who honestly cares? Your holiday/beliefs/religion are not tainted when someone different than you does not choose to reflect a casual intended-to-be-cheerful sentiment. But, why not say "Merry Christmas" if that's what I choose to celebrate? "Celebrate" is even a loose term. I watched Scrooged and had an apple pie, ya know? I have no plans to view a baby Jesus tomorrow.
I would not be offended if someone chose to wish me a holiday greeting of their choice (any time of year, not just in winter). I'd be totally a million percent happy to hear "Happy Purim!" from Jewish friends (or strangers). One of my students last term asked for Eid off this fall, and I enjoyed learning about it. For sure, she could write the in-class essay remotely.
But, I suppose I know that being a non-white non-Christian person in America is inherently difficult at times. Perhaps casual reminders that the majority of your culture believes something you don't is suffocating. I check my privilege here. I get it. I think I'm dreaming of the world I wish we lived in--where people would all openly say what they believe and how they choose to do so and we're all in awe of each other and how unique we all are...not the world we live in where people don't want to wish anyone a pleasant Ramadan because someone may want to kill them in response.