I'd say that except in absurdly extreme cases which don't actually exist (ie - "I am a muslim because that's the best way to worship Vishnu"), anyone who self-identifies as a Muslim can be considered a Muslim.
Depends on the purpose for which you are considering or using those categories. For the purpose of holding people accountable and expecting certain reactions from them when others use that label for heinous actions, then it probably is reasonable to expect those who identify as Muslim and defend the group against injustice should either take responsibility for or decry the actions of others who claim that identity is served by heinous acts.
However, as a matter of trying to accurate capture the content of a persons's traits, beliefs, and values that are related to those of the major institutions and documents that founded and historically shaped and promoted that identity, then what people say they are should be considered skeptically and as unreliable, only slightly less so than a women should take the word of a man in a bar who claims to be a pilot.
If two people with directly opposing views and values claim to be a Muslim, then it must be the case that either one or both are wrong, or that the label Muslim has no relationship to the views and values in question. In the case of extremists and moderates, either one or both are wrong or the label is largely meaningless and just a string of letters arbitrarily slapped onto to things.
In fact, of all the things people claim they are, their claims about religion are the least likely to be accurate. People have massive motive to pretend they are something they are not with regard to religion, and they have every means to get away with such deceits since it is very hard to verify the actual contents of their beliefs.
BTW, as I have argued often on this issue, objectively the extremists and fundamentalists have the most valid claims to their respective religious labels as their views and values and actions are objectively far more in line with those who originated and historically shaped the religions and the terms.