"I was wished a happy holiday by someone. I told this person I'm Christian and that it's OK to wish me a Merry Christmas."

Why not just accept their good wishes in the spirit in which they were intended instead of correcting them? Personally, what you did strikes me as a bit rude.

I don't give a fig whether somebody says Merry Christmas, Happy Holidays or Have a Nice Day. Unless I have some reason to doubt their goodwill, I'm just going to appreciate it. The last thing I'm going to do is assume some ulterior motive for the words they happened to choose.