Bill O’Reilly claims Christianity isn’t a religion

So a bunch of people around teh atheist interwebs have noticed a story about Bill O’Reilly claiming that Christianity isn’t a religion, it’s a philosophy. This is actually just a variation on a popular Christian meme, “Christianity isn’t a religion, it’s a personal relationship with God.” I also once heard a Muslim claim that Islam isn’t a religion, it’s a “way of life.”

One way to look at this, as an atheist, is to immediately declare victory over religion. I mean, if nowadays even conservative Christians see religion as a bad thing, we must be doing something right!

On the other hand, I really wonder what all the people who say things like this are thinking. It’s one thing to claim atheism is a religion, since it’s at least a stance on religious beliefs (though people ordinary use “religion” to mean more than that). But to claim Christianity isn’t a religion… Christianity is a paradigm case of a religion! How can it not be obvious to everyone who says this that they’re not just redefining words for the sake of rhetorical convenience?

I've read Draper's paper, and I am puzzled
Francis isn't the Pope the Catholic Church deserves, but the one it needs right now
Kris Komarnitsky's Doubting Jesus' Resurrection
Why do Christian philosophers of religion believe?