I dont' recall why it's acceptable for it to be called xmas... i'm positive if you really are interested you can find that kind of information on the web though.
But is it cheating yourself or your own religion if you celebrate xmas? I don't consider that. Would it be 'cheat' if white people celebrated Chinese New Year? Or for non-football players celebrated their city winning the Superbowl?
We're not Christian, but in my family Christmas was celebrated because it was fun, and because us kids should have a regular western upbringing. I've never been denied xmas by my family, but i would imagine if i did i would have felt really left out... all these other kids getting all sorts of presents, getting pictures with Santa, have big family get togethers, and you're without that? That'll be hard on a kid. Thankfully my parents had the insight to know that us kids should have it like everybody else.