You can figure out a lot about a society if you know what its members deem to be famous. Do they focus on spectacular athletic feats? Are they obsessed with the courage demonstrated in a battle? Do they sing praises to the wise elders of the community? Do their monuments point to a fascination with nature, or their own accomplishments? "Famous" touches on both human societies and the 'society' of nature.
Nye is telling us all about the downsides of fame in this poem. It's predatory, as with the cat and the birds, and creates divisions (like those between the boots and the dress shoes).
The seventh stanza refers to society's obsession with celebrity, wherein people "love" certain celebrities, hang posters of them on their walls, obsessively research their lives, and generally feel as though they "know" the celebrity.