I would identify three major themes of Gulliver's Travels that relate to the religious beliefs of Swift's time.
First, Swift was a devout Christian, a member of the Anglican Church. But from his writings, one gets the sense that he was leaning towards a more ecumenical form of Christianity in which Lilliputian-like differences of opinion between denominations would become unimportant and fade away. To Swift, these disputes were petty and "small," like the Lilliputians and their arguments among themselves.
Second, Swift's satirical "mirror" is meant to show the Europeans that their own behavior is hypocritical with regard to religion. The King of Brobdingnag famously tells Gulliver that the English (by extension Europeans in general) must be "pernicious odious vermin"...
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