I really don't care what people say, and odds are whatever it is I'll respond sincerely and cheerfully in kind.

That said, I do get a bit irritated when people make an effort to use my religion in the justifications for a non-specific greeting. For example, this year I saw just such a justification referencing, among other faiths and holidays, the potential hard feelings Muslims might experience over Eid and the Islamic new year not getting their due holiday recognition.
Now, Eid came and went right after Thanksgiving. And the Islamic new year is essentially a non-holiday, save for those sects which consider it the beginning of a month of mourning ... which, as you might imagine, probably doesn't fit that well with pretty bows and sparkly lights. To me
personally what the inclusion of Eid said is, "We're very happy to make room for your celebration at a time that has nothing to do with when it occurs and without reference to what it signifies to you." What the inclusion of the start of the Hijri calender said, to be frank, was, "We're C&P-ing December '09 holiday lists and don't actually care about the relative celebratory significance or even the meaning of what is being included."
The Islamic calender shifting as it does, next year I am quite sure I will find a similar list being passed around with the new year once again, and Ashura. And I am also just as sure that if I were to ask the people making such lists what Ashura is, for example, my question will be met with either the sound of crickets or the sound of letters being typed into Google's search box.
It's certainly all very well intended, so I wouldn't call it insulting outright ... but it is a manner of being "inclusive" that at times can be at least as minimizing as the alternative it proposes to supplant. In practice, in that manner at least, it feels more like a pat on the head from the dominant culture than any real effort to be diverse or to learn about what other people are all about. And personally, while as above I'm perfectly fine with "happy holidays," "seasons greetings," or what have you, if inclusivity is the goal I would be a lot happier saying "Merry Christmas" to those who celebrate and having them say "Happy Eid" to me when actually appropriate than us all exchanging generic phrases at Christmas time and everyone just assuming that somehow covers recognizing that occasions important to me exist.