Your weekly logical fallacy: no true scotsman
Oh this can be a fun one! At the same time it is easy to use in an argument. I recently saw a video where a Muslim caller asked an Atheist if they heard Allah's voice would they be convinced of a god. To which the host pointed out an issue and saying that if that person went down that path they might not be a Muslim. Thanks in part of the teachings of Muhammad. Someone could then turn around saying, but not all Muslims believe that. Ok, sure the difference is that it is dogmatic teaching and so the caller put himself in a trap. Not the example I am going to use so let's move on.
[You made what could be called an appeal to purity as a way to dismiss relevant criticisms or flaws of your argument./p]
In this form of faulty reasoning one's belief is rendered unfalsifiable because no matter how compelling the evidence is, one simply shifts the goalposts so that it wouldn't apply to a supposedly 'true' example. This kind of post-rationalization is a way of avoiding valid criticisms of one's argument.
Billy a nudist says that he likes to go nude at home, but that for some reason he didn't feel comfortable when he had to wear pants without boxers. Stacey a their generation nudist said that only a true nudist would dict underwear in all cases.
As a side note: This can also get into the idea of self identification. If someone identifies as a different gender than what is reported on their birth certificate, that's their identity. You have no right to tell someone they are a man or a woman anymore than someone has the right to tell you if you are a textile or not. At the end of the day we are all human and can represent ourselves the best we can.