As a non-Christian, being told to have a "Merry Christmas" in the States bothered me, but it doesn't bothered me here.
This is because "Christmas" seems to be much less religious here in the UK than in the US, at least in my experience.
In the US, lots of Christian religious imagery - manger scenes in front of people's homes, and so forth.
In the UK, it is more about spending lots of money on gifts, eating lots of food, and drinking lots of alcohol, which isn't specific to Christianity. Haven't noticed anything particularly religious (i.e. specifically relating to the birth of Jesus) about Christmas in the UK so far in the three years I've been here, other than TV specials about the life of Jesus which I can ignore. I don't count Christmas trees and Christmas lights as Christian symbols; they have more to do with the solstice than with Jesus, and we Jews suffer from SAD as much as anyone else.
It doesn't bother me to receive a Christmas card with a pretty lit-up tree on it as much as it does to receive a card with the Virgin Mary holding the Baby Jesus, with the Star of Bethlehem overhead.
That is probably just my personal experience, based on where I come from in the US and where I am living now in the UK.
Although, in general, I find that the UK tends to be more secular than the US, or at least in the UK religion is more private while in the US it is more public.