Church of England in Augustans
Church, monarchy, politics: it was all mixed up back during the Augustan age. The dominant church of the time in England was—you guessed it—the Church of England, a.k.a. the Anglican Church. The doctrines of this church were upheld by the monarch, and it was officially the "national" church.
It wasn't actually that simple, though. There were a whole lot of people, including some of the literary big shots of the Augustan age, who did not belong to the Church, or who disagreed with its doctrines. Some of these people were Puritans, some were Roman Catholics, and some were Protestants (called "dissenters" or "Nonconformists") who rejected some of the Church of England's doctrines.
Shmoops:
Daniel Defoe was a Nonconformist who was a big believer in religious freedom. In Defoe's novel Robinson Crusoe, the character Crusoe also allows for religious freedom on the island he inhabits.
Even believers in the Anglican Church, like Jonathan Swift, couldn't help criticizing some aspects of it. In A Modest Proposal, for example, Swift stick it to his fellow Anglicans for not caring about poor Irish people. Check it out an analysis of Swift's critique here.