Romantic poetry tends to be more subjective/emotional than objective/intellectual. Romantic poetry was a reaction against the reason of the Enlightenment. The emphasis of Romanticism was emotion and individualism. So, most of what is now considered “romantic” is subjective, introspective and emotional. A lot has to do with personal experience, themes in rural settings and individualism.
This poem is mostly subjective and emotional. The speaker says that the site of a rainbow currently makes his heart leap just as it did when he was a child. He hopes for the same effect when he is an older man. Wordsworth believed that a subjective outlook was preferable and that people were not as emotionally (or intellectually) restrained in rural and natural settings.
The speaker hopes his days are bound by this natural piety. On one hand, this means that he hopes his feelings of free expression and wonder with nature never leave him: his days are bound by this perspective. This is his personal, subjective way of engaging the world.
On the other hand, you could interpret this as a hint towards an objective in the sense that such a perspective could be shared by all people. Subjectivity implies difference between all individuals. Objectivity implies a truth that applies in all situations. The only way you can attribute this “personal love of nature” sentiment as an objective sentiment that may apply to all people is with line 7. “The child is the heart of man.” If he had said, “my child,” the poem would retain its complete subjectivity. But this statement is sweeping. It applies, or attempts to encourage the speaker’s sentiments to all “man” or human kind.
So, it is primarily subjective, but there is a subtle plea for objectivity; each individual is capable of this subjective and emotional perspective of nature.