AR,
That fallacy holds to a point. e.g with a Scotsman you can say by lineage he either is or is not. So if I said not true Scotsman is 100% German I would be correct. If we look at Christians there is a much fizzier line but there is a line non the less.
There are parts of Christian belief that are a must, deny these you deny the person of Christ and cease to be a Christian (though you may still be a nice guy and one heck of a line dancer). Then there are other points of debate which while interesting and heated is not an issue that should cause a party to leave or be removed from the church.
Example of the former: The nature of Christ is he (a) Devine, (b) eternally God from and for all time, (c) part of the triune God? If you say not he was not, you’re not a Christian.
Example of the later: The persistent virginity of Mary, If you think after the birth of Christ she had relations (as would seem to be indicated by Mark) it does not take away from the nature of God or Christ just as if you believe she abstained for her whole life.
And Fred Phelps fits that definition, thus technically Christian -- so he's right, I bashed a Christian. But I believe Phelps has definitely forgotten the morality as a whole that Christ taught. Strange, I don't have those three core beliefs, but I believe I act more inline with Christ's teachings than he does. I may not think he's a god, but you'd have to be an idiot (or a rabid anti-Christian) not to recognize him as one of the world's greatest moral teachers. Even the Muslims revere him.