holiday greetings

Sorry if this has been discussed before, but I've just had a quick look through the archives/tags and didn't find any posts relating to this topic.

I have been living in England for 16 years and still can't get over the way nearly all English people seem to presume you celebrate Christmas, wishing you "Happy Christmas" and asking you if you are "ready for Christmas?". This question is nonsensical for me because apart from sending a few cards and sometimes having a meal with friends, I don't celebrate Christmas. When I try to explain this people often seem taken aback, as if it is something very unusual. Because of this, I have mostly stopped explaining this to people and just answer their question with "yes" (because technically I am ready, since there is nothing for me to do!) and let them assume I celebrate Christmas.

Yet my recollection from growing up in the USA (mostly California) is that I was taught it is rude to assume people celebrate Christmas, as for example they might be Jewish. Now I am wondering, is my memory correct? Is it considered rude in the USA to assume people celebrate Christmas? I thought that's why people there wish each other "Happy Holidays" or "Seasons Greetings".