What are two examples of how Chaucer hints that people might not be going on the pilgrimage for spiritual and religious reasons, but more for social ones?
I think one example is his descriptions of everyone's clothing and social status.
Chaucer's Prologue to The Canterbury Tales lays the blueprint for his tales in which the characters interact and give rise to the satire and delightful, sometimes dark, and other times edifying, narratives. Two ways in which Chaucer suggests that some of the pilgrims may not be going to Canterbury for religious reasons are in the descriptions of what they wear and how they act.
One example is that of the Prioress, who is described with the contradictory term of "coy" which is not a quality of a religious person who is supposed to be humble and detached from the world and anything of a sexual nature. The Prioress is also vain as she "spoke daintily in French, extremely." In addition, she displays vanity as
She wore a coral trinket on her arm,
A set of beads, the gaudies tricked in green,
Whence hung a golden brooch of brightest sheen
On which there first was graven a crowned A,
And lower, Amore vincit omnia.
Her golden brooch is in violation of the vow of poverty that nuns must take; moreover, the curious inscription of "Love conquers all" raises a question about the other vow of chastity that nuns take.
Another example of a pilgrim who religious devotion is questionable is the Miller, a jolly and drunken reveler, who possesses a "mighty mouth" that has a "store/Of tavern stories, filthy in the main." He also likes "to play his bagpipes up and down." This description of bagpipes and playing them suggests that he is both gluttonous and lecherous.