I don't think I can sum it up much better than the Washington Free Beacon article linked in the OP. But I'll throw my hat into the ring.
I'll start with a few caveats. I LOVE "Die Hard." I contend that it is the greatest action movie ever made. And when push comes to shove, I'll pick it as my favorite movie, period. I've had many heated arguments with those foolish enough to argue against the American cinematic treasure that is "Die Hard."
That being said, I don't think it's a Christmas movie. Yes, it takes place at Christmas and, yes, there are Christmas references throughout. But Christmas is not central to the plot, the characters story, or really anything at all. "Die Hard" would be about 98% the same movie if it took place over July 4th weekend. You wouldn't even have to change the weather. Hell, "Die Hard 2" at least had snow. You wouldn't have a movie with: "Christmas Vacation" "A Year Without a Santa Claus" or "A Christmas Story" if they weren't about Christmas.
Put it this way "Die Hard" takes places at Christmas but it isn't about Christmas, in either a secular or religious way. It's not a Christmas movie. You can watch and enjoy it at any time on its merits as the pinnacle of the action genre so leave it at that. Yippee-Kai-Yay, IE. Beat USC!