But, of course, it is a religion and, no, it isn't a relationship. I have always felt, even when I was a believer, that this sort of language was an attempt to set themselves apart from other religions and even those they consider lesser versions of Christianity.
Anyway, I wrote this as a comment on a thread some years back and I think it sums up why the word relationship, in this context, doesn't work -
I have personal relationships with real live persons. We talk, and the conversation occurs on both sides. We do stuff together and there is interaction.
If I think I have a relationship with someone because I have read their book, or heard their music, or looked at their art - that is only occurring in my head. I have watched many Quentin T. movies and listened to scores of interviews with him... so much so, it feels like I know him. But I don't and he doesn't know me. It is a flight of fancy to imagine otherwise.
When Christians state that they have a relationship with God, they are using that word in such a way that it is rendered meaningless. Even if we imagine for a moment that there is a god that made the universe and he wrote a book for us to read, we could appreciate his art and read his writings... but we still would not know him and we would not have a "relationship" with him.
It seems to me the best thing a Christian could say in this regard is that they are a Christian because they work at following the teachings and life of Christ.