What is the connection between the pink ribbons and the two conceptions of faith? No.
Initially when Brown leaves his wife and her pink ribbons behind, they represent innocence. For when he leaves for the wilderness he is a much different man than when he returns. Brown's faith in his religion, town, wife, and destiny are firm. However, once he meets the devil in the wilderness, all those change. Finally, when he thinks he hears her voice in the woods and sees her ribbon descend from above, he cries, "My Faith is gone." Of course, his faith in all that he held dear - his religion, town, wife, and destiny is gone. Seeing that ribbon in the wilderness causes Brown to literally lose his faith and his innocence. Notice that now as he tears through the woods with the devil's second staff (Goody Cloyse took the first), Hawthorne observes that nothing in the wilderness - not the black mass nor the devil himself - was as frightening as Goodman Brown.