A narrow Fellow in the Grass Occasionally rides— (1-2)
The image of a narrow "fellow" lost in the grass is, without drawing you a picture, possibly a reference to intercourse. The mention of riding in line 2 only strengthens that possible interpretation.
A spotted Shaft is seen, (5)
Could this be a possible reference to the male anatomy? Some say "Yes!" Others say "Nay!" What say you?
Several of Nature’s People I know, and they know me (17-18)
You may have come across the phrase “to know someone in the biblical sense.” This is a polite way of suggesting a sexual relationship. So, to “know” someone could mean that this group, “Nature’s People,” and the speaker have a sexual past.
I feel for them a transport Of cordiality— (19-20)
These lines make perhaps the strongest case for a sexual interpretation of this poem. The speaker here is telling us that he feels some deep kinship for "Nature's People," a connection that would seem to surpass mere platonic friendship.