the point is moot because you can't label a group for anything unless the group promotes or allows it. islam does not promote 'jihad' any more than christianity promoted the crusades. both are examples as i have stated, of non-believers (or misled believers) using religion as an excuse for war.
unlike your so called scotsman fallacy, there is no dispute here. how one would define what constitutes a scotsman is ambiguous. however, christians are defined by their actions, in comparison with that which is taught in the Bible and by Jesus. thus with this comparison, one can indeed know whether someone is a true christian. no true christian would commit murder. if a "christian" murdered someone, they would be violating their belief in christianity, and thus cannot be called a christian, because their actions oppose it. in such a way, the above points i have made are valid.
what you fail to understand (or admit) is that religions have systems of beliefs, and anyone who does not match these beliefs and action in accordance, is not a member of that group. i don't care if they claim to be, i don't care if they change their legal names and write Jesus all over their car, house, and face. it is action that defines, not claim. when people commit crimes in the name of christianity, they are not christians. when people commit crimes in the name of islam, they are not muslims, so far as i understand their beliefs. if your religion allows for murder,then one can commit murder and still be a member. this is not the case with those you convict.
you are right that a religion is represented by its followers. i move to correct your assumption that this is all who claim to follow, instead i say it is represented by those who actually follow. if otherwise, it has no true identity.