From my British perspective, Christmas is already pretty much a secular holiday - I know Christians, Muslims, Jews, Sikhs and atheists who are all quite happy to send out cards, give presents, go to parties, put up decorations. Most of the cultural trappings of the festival have little or nothing to do with religion anyway: decorating a fir tree with sparkly tinsel, or pulling a paper tube with a small gunpowder charge and a silly hat inside have no significance in Christian doctrine that I'm aware of.

Besides, everybody knows that the Christians appropriated a pre-existing Midwinter holiday anyway, and a lot of the symbolism - [re]birth, light in the darkness, family coming together - is just as appropriate to a festival whose purpose is simply to mark the longest night of the year. Which doesn't, of course, explain why secular Australians still celebrate Christmas too. :-)

But when it comes to cultural appropriation, I'm pretty democratic. If enough people follow a tradition, then it becomes "their" tradition by definition, and any quibbling over its original derivation is irrelevant. It's as authentic as any other thing people do.