> I feel that there's a lot of truth to this, except that there are lots of actual Christians amongst the various denominations.
I don't think this is a good take. I think C. S. Lewis got in better in Mere Christianity:
> We must therefore stick to the original, obvious meaning. The name Christians was first given at Antioch (Acts xi. 26) to “the disciples,” to those who accepted the teaching of the apostles. There is no question of its being restricted to those who profited by that teaching as much as they should have. There is no question of its being extended to those who in some refined, spiritual, inward fashion were “far closer to the spirit of Christ” than the less satisfactory of the disciples. The point is not a theological or moral one. It is only a question of using words so that we can all understand what is being said. When a man who accepts the Christian doctrine lives unworthily of it, it is much clearer to say he is a bad Christian than to say he is not a Christian.
* https://en.wikipedia.org/wiki/Mere_Christianity
A "Christian" is someone who believes certain things (e.g., Nicene Creed), and that he should do (or not do) certain things. The inability to live up to one's ideals does mean you reject those ideals (or make them invalid).