Priest vs Cleric. Let's take Forgotten Realms into account. It's actually high but narrow magic, something that most people new to it don't know.
In FR, even in the Sword Coast, you won't walk into a village and have a Cleric. A priest, yes, but a priest has no magic. But not a Cleric. Clerics are few and chosen by the gods for their dedication. If you're there because your parents pushed you, because it was your only option, or, really, anything else that isn't 100% dedication, the god is going to ignore you.
Clerics (and also court Wizards) aren't even found in all the biggest cities. Sure Baldur's Gate has many, but that place is a hub for trouble that the gods and people want to keep locked and secured. Your average peasant wouldn't even know magic was a thing. So your level 1 adventurer going through and slinging Firebolt is as amazing to them as an archmage with meteor swarm is to the party.
But this depends on the setting. Eberron is a bit... Vague if gods even exist. If they don't power is fueled by belief not gods themselves. So if you half-ass it, you're not getting anything.
So why would a god choose someone who dislikes them as their champion? Is it that god's laws? Is it them personally? If so... What the fuck happened? Depending on how these are answered, it may be OK or bad. But most of the time it'll be bad.
As for Hades, he was liked, but not worshipped outside his cult. Unlike Zeus, he was seen as fair. He didn't unnecessarily punish because his ego. He gave people chances to prove worthy. When a king wasn't burried? Yea, go back and convince your wife to burry you. Might have been the king's trick and he was punished for it afterwards but he was fair. Same for Orpheus, or Heracles, or Odysseus, all who came to the underworld with a quest. He didn't help them, nor did he hinder them. He allowed them to do it and prove themselves.
His cult worshipped him in hopes of pleasing his so he would overlook some sins.