My wife is a Sikh and yet has no problem with the word Christmas or indeed wishing people a merry / happy Christmas. If people don't wish to send a card with the word Christmas on it then why bother to send a card at all? In all honesty I think the word Xmas is used because people are simply too lazy to spell out Christmas.
I agree that the true meaning of Christmas is often forgotten about but I don't think that is an excuse to start writing "Happy Xmas" in cards. If someone sent me a Happy Holidays card I'd assume that they were taking the ****.
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It might have been in use for 400 years but it still sounds cheap and nasty. It essentially say's that the person writing it can't be bothered, in which case they can't be bothered to do a lot of things in life. 'Can't be bothered' is something that lets our country down all the time.
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As far as I'm concerned you're allowed to have an opinion on anything but that doesn't mean to say that you are right.
I don't think the word Xmas has anything to do with popular culture;
I might have just turned 50 but I still have more than a grasp of popular culture