This is an interesting question because idealized ideas of what society should be are presented as often as actual ideas of society. Now, if you actually mean "ideas about society," both the idealized and the actual are covered. The first stanza presents an actual idea of society in that people do often call upon what religions recognize as the author of "Mercy, Pity, Peace, and Love" when in distress, and the well behaved then give thanks to "these virtues of delight" in return for aid. A poetic device that adds to the effectiveness of the presentation of this idea is that of repetition of the -s sound in the stanza 1 abcb rhyme: distress/thankfulness
The second stanza presents a limited idea of society in that most of the religious among society define God's attributes as including "Mercy, Pity, Peace, and Love." This first idealized idea is that "Man" (i.e., all humanity), created and cared for by God, is meant to be "Mercy, Pity, Peace, and Love" as well. A poetic device that lends to the effectiveness of the presentation of this idealized idea is repetition of the same grammatical pattern in lines 2 and 4:
Is God, our father dear,
Is Man, his child and care.
The last stanza presents another idealized idea of society in that it states all peoples are equally the form of "Man," being "Love, Mercy, Pity, Peace," and the dwelling place of God:
Where Mercy, Love, and Pity dwell
There God is dwelling too.
Stanza 4 of the five stanza lyric poem is the most interesting in terms of ideas and poetic devices. The idea presented is that when people in distress pray, they pray to "the human form divine." This reiterates the idea in stanza 3 that equates the attributes of humanity with the attributes of God, thus establishing humanity as the entity in position and with the power to fulfill the prayers of distress: this is an idealized, unrealized idea of society. The poetic device used here is antithesis. The end words, with a rhyme on the final sound -s, are antithetical to each other, are opposites of each other: distress/Peace.