To be sure, but it is unreasonable to claim that people are not Christian because they behave in manners that you do not want to associate with yourself. This is why the charge of No True Scotsman is valid.
The problem is that while the narrowness of the definition is common among Christians, the definitions themselves are largely incongruent. Witness the virulent disagreements among Protestants, Catholics, Mormons, etc.
That is another problem. You made claims as though a definition were already established and generally accepted, but it was not.
"Self-identifies as X" is a quality, and arguably the most important one in this instance.
For those who are not Christian, the behavior of people that identify as Christians generally defines what the term means. I'll stipulate that there are nuances among the general category "Christian" which we can distinguish, however, such that it might be reasonable to say that one type of Christian is different from another, but it is not for any one person to state categorically that certain groups of people are not Christians without first establishing a general agreement on minimally sufficient conditions to be so categorized, or excluded from that category.