In The Odyssey, piety involves way more than going to church on Sundays, and it has a lot more to do with your day-to-day actions than how you feel in your heart. Want to prove your piety to the gods? Better round up some goats, because you're going to need to get sacrificing. And feasting. And banqueting. And burying your friends properly. And making very sure that you never challenge and insult the gods in anyway. See? There's no way you could fit all that into an hour and a half on Sunday.
Humans in the Odyssey might revere the gods, but the gods see humans as hardly more than playthings.
Since Odysseus is so god-like, those who disrespect him suffer the same consequences as those who are impious.