When the author and speaker witness the city, it is asleep. It is not in its hustle-bustle busily polluting the environment state. The fog is still settled, the sun is just rising, and it is calm from his vantage point. Had he seen the city from the bridge at the height of activity, I doubt this poem would have been written.
Nature can be peaceful when it is quiet, and the city can be peaceful when quiet. The poem describes how a city has the same rhythms of nature. There have been other poems that do this more closely however. For example, the flow of a river and the flow of traffic. In that way, a city can be like nature.
I agree with Post #3 more than with Post #2. Wordsworth is clearly saying that the city, as it is right at this point, is beautiful and in tune with nature. He is saying, it would seem, that the city is only in tune with nature for so long as it is not awake.
So the brief answer to your question is that the city is in tune with nature because all of the people are asleep. Right now, the city could just be part of nature. But once the people come back on the scene, the illusion will be gone.
You might say that the city is like nature in this poem. Wordsworth’s poetry often celebrates nature, its quiet and solitude. The city is its polar opposite. However, in this poem, he is clearly in awe of the beauty of the city. However, he is viewing the city at its most nature-like time: in the early morning. There is no mention of the hustle and bustle of city life. The people are still asleep. He even describes the buildings as asleep. He does indicate that this beauty is fleeting. It will be gone when the city gets going.
This city now doth, like a garment, wear,
The beauty of the morning; silent, bear, (4-5).
It does seem odd to say that the city is in tune with nature. But maybe it is. Wordsworth certainly describes the city as he would describe nature in his other poems. In its sleeping state, the city is described as interacting with nature. The sun is shining on it. Industry has not yet begun, so there is no smoke. If the city is sleeping, it is breathing and alive, thus completing the personification that the Romantic poets often attributed to natural phenomena. I think you could say the city is in tune with nature in one respect and it is a stretch. If we say the people of the city, who are asleep, are in tune with nature, it is because they are asleep. They are not being social or industrial and the image of the city in the early morning reflects this. Being asleep, they are dreaming and breathing. These are somewhat like the elements of poetry and imagination that Wordsworth celebrated. His theory of poetry was centered on the individual imagination and that poetry was the spontaneous overflow of emotion reflected in tranquility. What could be a more appropriate way to describe an individual in the process of dreaming.
It is fleeting. And this is the only time when a city dweller (or the city itself) can be nature-like, or “in tune” with nature as you put it. As soon as the people get up and the factories fill the air with noise and smoke, that congestion will obscure any connection or comparison with nature.
I hate to disagree with the main point of your question, but I don't actually agree that this poem presents the city as being in tune with nature. I think that maybe you are confusing the comparisons that Wordsworth makes with nature with saying that the city is in tune with nature. Let us examine the relevant parts of the poem carefully:
Never did sun more beautifully steep
In his first splendour, valley, rock, or hill;
Ne'er saw I, never felt, a calm so deep!
Note here that although nature is obviously mentioned, Wordsworth is saying that the sun was never so beautiful shining over various aspects of nature such as valleys and hills as it is shining on London. Also, he says that he has never felt a calm so deep as looking at the sight of London he is contemplating now. So, the poem does not actually say that the city is in tune with nature. Rather, nature is used as part of the way Wordsworth presents the beauty of the view.