Whenever someone wishes me a "Happy Holidays," I always make sure I tell them MERRY CHRISTMAS in a stern voice. I do not wish for them to inflict their political correctness agenda on me and my country and my culture. It's offensive to me. I don't even take Happy Holidays folks seriously, because it's done to try to intimidate Christians or even secular Christmas celebrants.
I have seen the term "holiday tree," "holiday cookies," GAG---I mean really?? It's political correctness run amok. OP has it right.
I definitely agree with you regarding the second paragraph. Political correctness has gone berserk.
As for the first paragraph, it's best to use "happy holidays" as the default greeting if you work in customer service or if you're in public because you might not actually know what the person celebrates.
If you're in a room full of people that celebrate Christmas or if you're greeting a bunch of relatives who celebrate it, don't be afraid of saying "Merry Christmas".
What is annoying are people that insist on always saying "happy holidays" even if you're saying "Merry Christmas" to your own mother in, say, New York City.
And can we address how some people are trying to replace "snowman" with "snowperson" in the English language? The English language wasn't built to be politically correct. Get over it.