I guess what gets me is that if one of the ways to develop an understanding of the question is to look at the way the sides treat the other, there's something interesting going on with this one.
It's a relationship. I hate religion. It's man made and it kills and it's bad.
It's both. You can't have Christianity without a relationship with Christ...but you also can't have that relationship if you don't have the terms of that relationship - defined by the religion.
Religion: worship of a deity - a set of common beliefs about that deity. Augustine wrote about "religion" having the meaning of "being bound fast"
As a people of God, we are all bound fast by our common beliefs in God: The deity of Christ and the death, burial and resurrection of Christ being central.
"Religion" is "us-centered." We are one church, one bride, one family of God.
"Relationship" is "me-centered" - my Jesus, my relationship. (note: that's not a bad thing, that personal relationship is as necessary as the "us" piece.)
I saw a baby dedication this past weekend. The thought struck me then: if there is no "bound togetherness of shared beliefs" - why have the congregation commit to helping the parents (the "us piece" bring that child up in those beliefs?
It's got to be both? You have a relationship with your spouse; it's the marriage covenant that defines what that relationship looks like.
You have a relationship with Christ; its the terms of the Christian religion that defines what that relationship looks like.