I too do not have a problem with Happy Holidays --- I believe it was derived from Happy Holy Days, but I could be wrong.
What I have a problem with really is when they are 100% against Christmas, or Hannukah, etc. And want to have whatever they want at the expense of what I want. That is what irks me.
I have Jewish friends that wish me a Merry Christmas and I will them a Happy Hannukah. I could easily wish them Happy Holidays as their holiday is a Holy Day for them.
Yes, the word "holiday" is derived from "Holy Day" from medieval times.
I think that was the show where Fonzie jumped the shark and the gefilte fish, while singing Silent Night. ;)