Is Ginsberg really a religious poet, or is he just "spiritual," which is a word we sometimes use to describe people who seem to believe in "something," only we're not sure what? After all, the speaker of Howl seems to cherry-pick names and symbols from many religious traditions, from Kabbalah to Islam to Christianity. Plus, many lines in the poem would be considered heresy by orthodox religions, such as when the speaker suggests that we don't need the idea of a "supernatural" Jesus. Nonetheless, there's a strong case to be made for the idea that Ginsberg is a religious poet. Specifically, he can be considered a "mystic," which means he's not interested in patiently following the rules and dogmas set down by tradition. He wants communion with God or a higher power. Other notable mystic poets like this include Dante and William Blake.
The speaker does not follow any particular religious creed, but he does believe in something called "the Supernatural."