If person A gives a generalization about a category of people, person B gives a counterexample (which is an exception to the supposedly exceptionless generalization), and then person A defines away the counterexample, then that’s the famous no-true-Scotsman fallacy: “No Scotsman puts sugar on his porridge,” person A says. “But my uncle Angus is a Scotsman, and he puts sugar on his porridge,” person B replies. “But no true Scotsman puts sugar on his porridge,” person A replies to the reply.
Contrary to the mainstream, though: Whether person A’s no-true-Scotsman move is fallacious depends on their definition of the term “Scotsman.” If their definition is, say, “has a Scottish passport,” then yes, their move is fallacious: Person B’s uncle Angus, who puts sugar on his porridge—that fact isn’t in contention in the dialogue given above—either has a Scottish passport or not. And if he does, then he’s an exception, a counterexample. He disproves the generalization. But what if person A’s definition isn’t like that? What if person A’s definition is instead identity-related? For example: “No Christian believes in polytheism.” “But my uncle John is a Christian, and he believes in polytheism.” “But no true Christian believes in polytheism.” There’s nothing fallacious about that. Put differently: “Your uncle John believes in polytheism? No Christian believes in polytheism, definitionally speaking, and thus he’s not a Christian.” The term “Christian” in that context is a group identity that’s defined in part as excluding polytheists from the group.
The question of whether to believe in polytheism is of course much more profound than the question of whether to put sugar on your porridge—that’s why the idea of denying polytheists the right to identify as Christian is so much easier to take seriously than the idea of denying people who put sugar on their porridge the right to identify as Scotsmen—but the logic is the same: The no-true Scotsman (or “no-true-Christian”) move is fallacious only insofar as the definition of the term for the category of people isn’t an identity. Otherwise it’s just person A being inclusive and person B being exclusive.
See below for elaboration on non-tautologically and tautologically true generalization about people: