I don't know about you, but I've heard this particular evangelical talking-point more times than I can count. It "preaches" well (perhaps not least because of the convenient "rel-" alliteration), and on at least one important level, I think it's intended to highlight the central place that Christians, perhaps Evangelical Christians in particular, put on having a personal relationship with Jesus Christ (I almost put that in quotes, too, as those words are used in precisely that way so often). I agree with the essential need for knowing Christ in such a personal way. Something that goes deeper than mere assent to a list of facts about who or what Christ is. Without that relationship, our faith is indeed empty.
But there's a sense which, these days, I am deeply troubled whenever I hear someone use those words. I don't get the sense that the speaker is promoting the value of relationship, so much as they're rejecting the idea of Christianity as a religion. Indeed, many Evangelicals are quite explicit on this point. Religion is something bad. Something to be rejected. That others might consider their faith in Christ as a "religion" leaves a bad taste in their mouths, and they are very quick to spit it out.
I want to push back on that idea just a bit. To the extent that this dictionary definition of the word "religion" is correct...
belief in, worship of, or obedience to a supernatural power or powers considered to be divine or to have control of human destiny...and to the extent that Christians believe that Jesus Christ is divine, Christianity is a religion. Any attempt to argue otherwise is simply to be in denial, and I fear that denial of such an obvious fact simply makes us look untrustworthy.
There is, of course, plenty of room to debate the precise meaning of Christ's divinity, and plenty of room to debate whether or not the word "religion" contains additional definitions that may or may not be desirable. But at the core of what Christianity and religion are, there really isn't any getting around the fact that Christianity is a religion.
So, why are so many people so keen to argue otherwise? I imagine that the answer to that is pretty obvious. The dangers of religious extremism are well-known (indeed, they already were well before 9/11, and I've certainly heard the "not religion/relationship" bit well before then), and most Christians understand that "legalism" is a bad thing and can lead to various abuses (even the ones who could be argued to be too legalistic!). Christians rightly seek to shift the folks away from "rules," and even from specific doctrines, and instead focus on the person of Jesus Christ, and the story of what Christ has done for us.
Especially as we enter into Holy Week, that story takes on special importance. But even the "story" itself could become flat—nothing more than a script whereby all the right words are memorized and repeated—if one forgets that a story has a particularly relational quality. There is an interaction between the person telling the story and the person listening to it that is essential to making a story work.
I believe that remembering this relationship—the one between ourselves and those who we would share our story with—is essential to getting the relationship we claim to have with Jesus Christ right. Especially if we consider the Church to be the body of Christ, the people of God are the only flesh-and-blood Christ we are likely to come in contact with (doctrines behind the bread and wine of communion notwithstanding). As we focus on our relationships with each other, we focus on our relationship with Christ, and as we neglect our relationships with each other, so also we neglect our relationship with Christ.
Perhaps as we renew that focus, strengthening our relationships with those other human beings Christ might claim as his own, the need to repudiate the idea of Christianity as "religion" will become less desirable.