The classic example of the "No True Scotsman" fallacy, from whence it derives its name, is this: McBeth claims that a Scotsman will invariably eat haggis regularly. McDuff replies that he's a Scotsman and he never eats haggis. McBeth retorts "Well then, you're not a true Scotsman". The "No True Scotsman" fallacy is a species of circular reasoning where the premise is redefined to exclude any inconvenient deviations and contradictions. This is a pretty common fallacy employed by Christians who by and large adhere to the "love thy neighbor" ethos against coreligionists who don't. When someone points out the horrible behavior of a group of Christians, you can be sure that someone will claim that "they're not really Christians because true Christians wouldn't act like that".
Of course, Love Thy Neighbor Christians will argue that they're not the ones deciding who are true Christians and who aren't, God has set the standards in The Bible. The trouble with that, as I have pointed out many times in this series, is that the Bible isn't clear or unambiguous in what it has to say. In addition, "Christian" is as much a cultural identifier as a set of religious doctrines and behaviors. Anyone who says they're a Christian is a Christian. One might argue whether a particular Christian is living up to some perceived Biblical standard, but that doesn't make them Not A Christian, any more than abstaining from haggis makes an Edinburgh native whose roots go back many generations Not A True Scotsman.
This doesn't mean that the Love Thy Neighbor Christians don't have a good reason to be embarrassed by the antics of their bigoted, hateful brethren. Like a family of cops who have that one sibling who just got out of prison, they think they're making them look bad. Guilt by association. But these hypothetical cops don't claim that their ex-con brother isn't their brother. But Christians are trying to boost their godliness average by eliminating their more embarrassing brethren from the statistics.
This is by no means a Christians-only phenomena. Fundamentalist Muslims who require their women to wear a hijab look down on the Muslims who don't as not true Muslims and the burqa-wearing sects are sure the rest of the Muslim world are just as damned as Christians and Jews, maybe more so. Ultra-Orthodox Jews are pretty judgmental about their Conservative and Reform branches - some don't recognize weddings officiated by non-Orthodox rabbis. Heck, I've even encountered this tendency among pagans! But since Christians are the power wielding majority in this country, this is whom I'm focusing on.
The truth is, that between Fundamentalist Evangelicals, Conservative Traditional Catholics, Mega Church Pastors and the like, cultural Christians who identify as right wing conservatives and espouse beliefs largely divorced from the Love Thy Neighbor morality are likely the majority of self-identified Christians in the United States. You can't just pretend they're not the face of 21st Century Christianity.