Whitman was not thrilled by organized religion. He was more of a mystic. Mysticism refers to direct contact with the divine and unity with God. The speaker calls his connection with the night air "mystical," implying that God exists within and through nature. Whereas the astronomer might argue that his abstract knowledge amounts to a contemplation of divine and eternal things, Whitman affirms the importance of the body and the senses over the mind. You could call Whitman's spirituality "democratic," in that it is completely accessible to common people in its most advanced and powerful forms. You do not have to follow a particular sect or creed to experience it.
The poem compares hierarchical religious ceremony unfavorably with democratic mysticism.
The speaker's escape from the lecture amounts to a flight from adult responsibilities in an impossible attempt to reclaim the safety of childhood.