A Jewish person, seeing that my ancestors were Christian for centuries, and that I celebrate Christmas, would call me Christian.
A devout and conservative Christian, seeing that I don't consider Jesus to be my personal savior, nor the Bible to be the word of God, would say that I am not a Christian.
Some, seeing that I practice an earth-centered religion inspired by pre-Christian traditions, might call me a Pagan.
Others, seeing that I don't believe in gods or magick, might say I'm not a Pagan.
Sometimes we change, but other times, we stay the same as the words attached to us shift, depending on who is doing the attaching.
If a person sees who I am, I don't really care if they call me Christian or not-Christian, Pagan or not-Pagan. If they see who I am, then the words they choose to apply vart depending on how they define the words.