"...A person's religion need not be his or her all-encompassing and exclusive identity. Islam, as a religion, does not obliterate responsible choice for Muslims in many spheres of life. Indeed, it is possible for one Muslim to take a confrontational view and another to be thoroughly tolerant of heterodoxy without either of them ceasing to be a Muslim for that reason alone..."Here's the article from Slate.com.
Limiting a given individual's identity to a unique and exclusive association may disadvantage both the individual and the institution he or she is associated with.
When somebody commits terrorism and it turns out he or she is a Muslim, reductionists conclude: Islam is bad. This is an example of how an institution is disadvantaged by a unique, exclusive identity association.
As for how the effect harms the other way, think about the stigma from which Islam now has to suffer, thanks to reductionist way of thinking. Somehow every muslim is a terrorist.
Of course it is easy to find examples showing that the effect can be good. Sen uses Al-Ikhwarizmi as an example. He's a great mathematician and he's a muslim. I can't blame muslims who are proud of this. But saying that every muslim is a good mathematician is simply wrong, no matter how good it sounds.