If your argument is:
Person A calls themselves a Muslim.
Person B calls themselves a Muslim.
Because Person A is a Muslim, Person A has subjectively defined what it means to be Muslim.
Person B does not Person A's criteria.
Person A declares Person B is not a a real Muslim.
Then:
By the same rationale, Person B also has a subjective definition of "Muslim" and likely doesn't consider Person A a real Muslim, either. If one of these people is correct and other not, then there must exist some objective measure of what makes a Muslim.
Personally, I don't think there is a reliable objective measure of the term. All religious people interpret their religions selectively, and there is simply too much variance across language, culture, and geography to define "Islam" propositionally. "A follower of the alleged prophet Mohammed" is about as specific as you can get. If ISIS says they are Muslim, and much of what they've done is enforce 7th century Islamic jurisprudence on their conquered lands, then, yeah, I kinda think they are really Muslim, regardless of what some other Muslims might say.
And again, I don't take this position to generalize the behavior of Muslims. I don't think this should inform foreign or domestic policy. I bring it up because Islamisim is a problem with causes far more complex than many here would prefer to admit. Yes, American foreign policy is a component, and that's what should concern Americans the most, but there are factors indemic to the Islamic world that need to be addressed, like poverty, education, institutional corruption, and a long history of sectarian conflict... And that kind of conflict usually starts when Person A claims sole ownership of the truth and proclaims Person B a fake.
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