My thought is that a better example with which to examine this premise would be the oneness Pentecostals. Doctrine-wise, they line up 95-99% with me. Their worship is awesome. They love Jesus--oh do they love Jesus. They are conservative, biblical literalists, and they do Pentecost they way we use to do it. BUT, they deny the Trinity. If I were to officiate a baptism using their formula ("I baptize you in the name of Jesus, for the remission of sins) I would be defrocked. So, are they Christians? I suppose C.S. Lewis would say no. Many of the groups you consider "Anti" would deny them as well. I'm pretty sure they would be denied membership in the National or World Council of Churches. Again...are they Christian? If doctrinal orthodoxy determines the word's meaning, then no. If it is something else, then maybe or probably.
Honestly...I don't argue the word. If Lewis is right, then the word does not refer to "what Jesus actually taught," because by that definition Muslims could be Christian. After all, they argue that Jesus never claimed to be the Son of God, and that his disciples corrupted his message. If Lewis is wrong, and the word's meaning based on anything subjective, then, like the word "gentlemen," just about anyone can use it, but the word becomes most imprecise in meaning. I suspect that's where the larger Christian world is heading--to a very broad, all-encompassing definition--one that includes rather than excludes.
To get at where someone is really at, the term Christian will need to be followed up with, "What kind?"
One more example. A guy at work told me he was Catholic, but that he disagreed with some of the church's teachings. Which ones? Abortion, birth control, gay marriage, etc. etc. I quipped, "Are you a Christmas/Easter only Catholic?" He look a bit embarrassed and said, "Well...I don't really go that often."