No, it doesn't make a whole lot of sense to me either.
"You load up on holiday ornaments, holiday bows, holiday lighting, holiday wreaths, holiday Santas and even holiday trees! And then it occurs to you, which holiday do they mean?!" states one page on the site. "Surely, no one would think of renaming the [Jewish] menorah the 'holiday candelabra,' nor should they. People of the other religions and cultures would never tolerate such revisionism, yet why do we? Perhaps, more importantly, why do they think they can get away with it?"
Let's see... referring to "holiday bows" is just as offensive as referring to "holiday candelabras." That's because the "holiday candelabra" is really a menorah, a symbol that has a lot of religious significance for Jews - renaming it means ignoring that religious significance and pretending that it doesn't exist.
Therefore, to devout and conservative Christians, all of these (apparently) secular ornaments, bows, lights, and wreaths actually have significant religious meaning! Why, it's just like saying "holiday barnyard" instead of creche and "holiday stick" instead of crucifix!
Like I said, it doesn't make much sense to me, either. I'd expect devout Christians who are serious about retaining the religious meaning of their Christmas would be quite pleased to see the word "Christmas" dropped from what are obviously secular observances, secular celebration, and secular symbols. When this happens, it becomes more difficult for people to confuse those secular aspects with the original religious holiday.
Personally, I'm not bothered with such confusion because I'm not personally bothered if the religious origins of Christmas end up being ignored by most people. I ignore them, so why would I mind if others do so as well? I'm just saying that I wouldn't expect devout Christians to favor anything that would aid in this process.