John Berryman wrote in the 20th century, which means that Puritans who lived in the 17th century could not have read his works. However, we can imagine what their reaction would have been like.
Berryman wrote in a "confessional" style. This means that his poems resembled confessions. He talked about his own personal issues and struggles, sometimes with topics that are considered taboo.
It is likely that the Puritans would have found these topics to be too inappropriate to be widely discussed and distributed. Moreover, the fact that the poems are so personal and not necessarily critical might have appeared to be self-indulgent to the Puritans.