I am not sure if Nick is entirely objective because he recognizes the inauthenticity of the social order in which he is a part. As the novel progresses, Nick strives to be a part of the social order of Tom, Daisy, and Jordan. It is through the experience of interacting with this setting that he ends up recognizing the phoniness and inauthentic nature of these surroundings. At the same time, Nick is one of the few characters in the novel to fully understand Gatsby as a person as opposed to an icon or symbol of wealth and prosperity. He understands his motivations and his personality well enough to suggest to him before his death that he is "better than the lot of them." In the end, Nick's desire to leave this social order, repudiating it once and for all, demonstrates his lack of detachment.
Nick in The Great Gatsby doesn't continue to be an objective narrator because he never is. He's opinionated right from the start.
A person who doesn't make initial judgments doesn't have to concentrate on not making initial judgments. When Nick opens the book telling the reader that his father taught him to not judge others, he is revealing that he and his father think they're better than other people. If not, why would they have to consciously try to stop themselves from making judgments?
Just look at Nick's dislike of Tom evident in chapter one. Nick is judgmental. The first time he sees Jordan he thinks she is arrogant and lazy. That's a first impression, which Nick says he never makes.
Nick is an unreliable narrator, and he's definitely opinionated and judgmental.
Although Nick says he is only honest person he has ever met, he is not objective.
Reason #1: He chooses sides. He aligns himself with Gatsby, a known gangster. He arranges an affair at his own bungalow between Gatsby and Daisy. Nick hates Tom and wants Gatsby to steal his girl. Nick knows that Daisy is only fantasy to Gatsby, yet Nick perpetuates Gatsby's fantasy life more than he tries to clarify or stop it.
Reason #2: He fails to intervene or become a moral agent in the novel. He knows Tom is having an affair with Myrtle. Does he try to stop it? No, he attends their party and watches her get slapped. He knows Jordan and Gatsby are both dishonest; he associates with them willingly.
Reason #3: He does not prevent tragedy; he does not even reveal tragedy. Nick lets Gatsby get killed without warning him in advance. He lets Tom get away without punishment. In the end, two dead men cancel each other out, and Nick accepts this. Nick does not tell anyone any of this, not even Gatsby's father at the funeral. He would rather have his father think his son was one thing, when, in fact, he was quite the other. Again, Nick perpetuates Gatsby's fantasy more than he tries to clarify it.