I think that the wording of the question is interesting. On some level, the novel shows how one's identity is that of an outsider if an individual is committed to seeing life in oppositional terms. Changez is seeking to find some realm where he is not an outsider. This is the result of him seeing the world in terms of "insider" and "outsider." It is evident that he is an outsider in America. It is evident that he is an outsider at Underwood- Samson. It is evident that he is an outsider with Erica. Each of these realities are ones in which is identity is that of an outsider. This is because Changez sees only duality in these worlds, and not the nuanced elements that might transcend them. Part of the reason he embraces fundamentalism is to avoid this condition of being an outsider. He wishes to be an "insider" and he believes that fundamentalism gives him the best chance of doing this. However, even in this, he is a "reluctant fundamentalist," something preventing him from full immersion and this lack of totality is where even here, Changez could be seen as an outsider. Changez, and human consciousness, will always be an outsider if it can only view reality in terms such as "insider" and "outsider."
I think that the work reflects how one's identity ends up influencing the individual to end up seeing themselves as an outsider. Changez sees the world in such stark opposition, dualities in which direct reality results from where one is placed. In this notion, Changez's identity strongly influences him in feeling as an outsider. His perception of the world and his place in it is one in which individuals are accepted or rejected. For Changez, his own identity and the manner in which he appropriates or understands the world is one in which he sees himself as an outsider. While he seems to be culturally at home as he tells the story to the American, there is still "reluctance" evident, and thus, an outsider element is still present. His identity, built upon binary construction, still influences him as being an outsider, even when he realistically no longer needs to be one. In this, Hamid is making the case that one's identity can exert a large influence in being an outsider if one is so strongly wedded to such a notion. It is only through escaping such oppositional distinctions that one might be able to transcend such conditions.