Legitimate question. I'd say a "fake" is one who picks and chooses what he/she personally believes to be true and valid. Similar to a "fake" atheist, who denies the existence of God but believes in, say, Angels or some subset component or group of components custom-chosen individually by the person. It is inherently inconsistent and contradictory, but many choose to overlook this.
While they may overlap, they are certainly not what I take it you are attempting to distinguish as "real" Christians. A real Christian would be someone that believes and accepts as true all the doctrines of Christ's Church started on earth.
Which of course begs the question of which of the thousands of Christian Churches did Jesus Christ start? The answer is only one.
While there is certainly some good in some of what has been done by members who protest Christ's Church, and there has certainly been bad behaviour by some human leaders from Christ's Church from time to time, as in every large organization, especially one that has existed over two thousand consecutive years and counting, and most egregiously in every man-made form of government.
Someone who protests that they agree with most but not all is by definition not anything but less than the whole. While less is certainly not nothing, it is less.
For your consideration:
http://www.catholicscomehome.org/who-sta...ur-church/
contains a PDF graphic chart that is more descriptive of men who thought they could do better than Jesus Christ did.
Interesting aside, in past research, I discovered that Methodists apparently no longer officially follow or use the original method that they were named after and founded upon to distinguish them from the Catholic Church. It appears to be more of a "club" approach. Church of England was founded upon the divorce of the English King Henry VIII; Anglicans and Episcopals are derivatives of these protesters. Etc...