I'm a Christmas-celebrating Catholic and I say "Happy Holidays". This notion that the words "Happy Holidays" are a political statement is bullshit. People said them long before Bill O'Reilly declared that there was a war on Christmas.
It's not "politically incorrect" or offensive to say "Merry Christmas" to someone who isn't celebrating Christmas (or, as is far more likely now, is instead preparing to celebrate New Years). It's stupid.
If I was in China, I wouldn't say it. In North America, I'm safe in assuming they're at least celebrating New Years, because they're probably getting the day off.
It's not "politically incorrect" or offensive to say "Merry Christmas" to someone who isn't celebrating Christmas (or, as is far more likely now, is instead preparing to celebrate New Years). It's stupid.