For a very long time Christmas was a minor Christian holiday (just as Chanukah was--and to some degree still is--a minor Jewish one). The whole point of Christianity is the Easter story--even a lot of Christians saw/see the various Christmas stories just as pleasant fairy tales--and so Easter was *the* Christian holiday. [Note, for instance, that Haendel's Messiah is actually an Easter oratorio.]
But over the last century or two, commercialization has turned Xmas into the nation's #1 holiday--just as more recent commercialization has made Hallowe'en #2 (Easter used to be)--and has even made Chanukah a much bigger deal than its religious significance would suggest.
I live in NYC and we have a lot of people celebrating a lot of holidays. I mostly go with "happy holidays"* just so I can say one thing over the course of several weeks--though on Dec. 24/25 I'm much more likely to say "merry Christmas," and in the last days of Dec./first days of Jan. I'll go with "happy new year."
I know a few Christians who are always ready to call Islam the Religion of Permanent Offense, and to mock ethnic minorities who seem to have donned the mantle of permanent victimhood--yet are mightily bothered by what they call the War on Christianity (which is really a "war," if that's even the right word, just against entrenched Christian *privilege*). But this describes only a few Christians. The great majority are just fine with "happy holidays."
*I've actually started saying "have a happy" and am going to try to make that a habit. Seems like it'll save a lot of time and bother.