I'm personally not offended when someone says Happy Holidays. It's not a new term invented recently, look at Christmas cards from the 1940s or 50s and you will see Season's Greetings, and Happy Holidays on a huge percentage of them. Also a period of when the popularity of Santa, a jolly old elf really exploded.
And in "Holidays", the meaning "Holy Days" is still there unless we are such an uptight Christian that we are blinded to it. What does bother me though is when a corporation dictates that their employees must not use the word Christmas. But rather than being rude to the employee, I think I'm a better representative of my Christian Faith when I smile back to them, and say "thank you, and a Merry Christmas and Happy Holidays to you."