People who say "Happy Holidays" aren't dissing Christmas. It's merely an acknowledgment that most religions and cultures have some sort of celebration around the winter solstice, and it's not always known what, if any, of these another person observes. So saying "Happy Holidays" is a thoughtful catch-all.
Also, no one is afraid of or resents the word Christmas. If the word is being dodged, it's for the same reason above: inclusivity. Anyone who is specifically referring to the holiday that celebrates the birth of Jesus (regardless of faith) will say Christmas or one of its other popular names.
Which brings me to Xmas. It is not an attempt to take Christ out of Christmas. X is the first letter of Christ's name in Greek, and ancient Greco-Roman catacombs often sported a giant X both to celebrate Jesus and to resemble the cross on which he was crucified. So instead of being blasphemous, Xmas is actually as holy an abbreviation as it gets. It's surely more majestic than C-mas, which sounds like a censored abbreviation that should itself be censored.
There is no war on Christmas, at least one that two sides are actually fighting. Wars on high prices? Definitely.