Oh, I think there's more than that. It's somehow not divisive for Jews to congratulate wide audiences with Hanukah. It's not divisive for Muslims to congratulate their audiences with Ramadan. It's not divisive for Chinese to wish others with happy Chinese New Year. But it's somehow "problematic" to say "Merry Christmas".
In all honesty, I can't imagine being offended if someone congratulated me with a holiday they celebrate and I don't. I would congratulate them back and maybe ask how they celebrate it to learn something new. On the other hand, if the Christmas experience was something the previous generation used to have, and I got priced out of it, "Merry Christmas" would sound like someone is rubbing it in...