The narrator of The Stranger by Albert Camus is Meursault, and he is, indeed, isolated from the world around him. This isolation is clearly a choice, something he chose for his life long before we ever meet him. His isolation can also be read as passivity (simply not making choices and letting life just kind of happen), but of course passivity is a choice, as well. Clearly Meursault chooses his own isolation.
We see this aspect of his life in every major relationship in Meursault's life. The first is his relationship with his mother. It is a distressing and emotional thing for most people to lose their mothers; however, Meursault is unmoved by his mother's death. He is emotionless during the ritual of burial, but of course that is because he was disconnected from her even when she was alive. He says:
It occurred to me that anyway one more Sunday was over that Maman was buried now, that I was going back to work, and that, really, nothing had changed.
His statement, that nothing had changed after her death and burial, can only be true if he felt nothing for her before she died, as well.
His relationship with Raymond Sintes is also an example of Meursault's isolationist worldview. Our narrator says:
he asked me again if I wanted to be pals. I said it was fine with me: he seemed pleased.
For most of us, this complete lack of enthusiasm about a friendship would make us question whether we actually had a friendship at all. Meursault does not really accept the offer of friendship as much as he simply lets the other man make a choice to be his friend. Meursault would have been just as happy without any relationship or connection to Sintes.
Meursault's does not treat his girlfriend any better than he treats Sintes. He is careless with her in nearly every way, and to call what they have a true relationship would be an awful exaggeration. Here is one example of his passive feelings toward her:
That evening Marie came by to see me and asked me if I wanted to marry her. I said it didn’t make any difference to me and that we could if she wanted to. Then she wanted to know if I loved her. I answered the same way I had the last time, that it didn’t mean anything but that I probably didn’t love her. "So why marry me, then?" she said. I explained to her that it didn’t really matter and that if she wanted to, we could get married.
His detachment is obvious, and Marie's willingness to accept so little from Meursault is painful for us to read.
Meursault is an existentialist, someone who believes that nothing is certain except for death: there is nothing after death, and life before that is nothing but hopeless. This philosophy does breed passivity and indifference, the precursors (or perhaps the causes) of Meursault's isolationism.
The inevitable result of living consistently with this worldview is that nothing matters. This is why Meursault does not care about friends, about love, or about death. Life, his own or others', does not particularly matter to him, and that is evident by Meurcault's actions in this story.
He is cruel and helps others be cruel; he murders a man; he does not try to defend himself even when he knows it could help save his life; he spurns the efforts of the priest who tries to save his soul; and he does not care if he dies. His isolation eventually kills him; the only positive in this is that he is not surprised or dismayed when he has to face death.
Meursault is a man who shies away from other people. He prefers to watch others than be the center of attention. He is an apathetic and nihilistic who doesn't see the point of interacting with irrational humans seeing as he is such a rational person himself. He believes in telling the whole truth with no bias but society is not built like that so he is always a bit isolated from the rest of the world.