Those names we choose to represent ourselves are ours to defend as we will, but defend them we must. I am an Objectivist; I have chosen this name for myself, and thus I cannot claim to be above what others who choose to use that same name may say or do. I have chosen to hinge my reputation on that name; it would be ridiculous of me to disclaim its effects on my reputation.
Thus I regard Muslims as having a duty, insofar as they wish to self-identify as Muslims, to defend the name; they cannot complain that others who share naught but a name with them do horrible things, and their reputations are tarnished, for that is the nature of taking umbrage beneath a name.
In the same fashion, I regard it as duty to take fellow Objecivists, and to a lesser extend libertarians, to task for their statements, and regard it as rightful to take pride when we behave as we should, and shame when we shouldn't. I am a member of this group by my own will, and contribute to it in my successes, and subtract from it with my failures.
And thus, while I previously regarded the actions of Ayn Rand and her followers in expelling individuals from her group as rather frightful and cultish, in my modern considerations I must conclude their behavior entirely appropriate.
It is wrong to suppose that a group exists independently of its members - a group is defined by its members, and where that group is inclusive, rather than exclusive - as is true of most political parties in most countries, every philosophy, and most religions - you basically have to live with what other people say or do, and if you don't want it to reflect upon you, react to it.
Or divorce yourself from groups. Those are your options.