I don't really have any disagreement here. Most of the players have a decent detailed backstory for their characters which I weave in and out of the main campaign meta-plot and they decide when to actively pursue such goals balancing it up with the stakes of the meta-plot. But everything is pretty much their decision. There is one player though that doesn't have any strong goals besides those provided by the DM and other characters' goals.
There is always one.... lol.
The way I understood it from the player, his character was forged by Kelemvor, instead of having his soul spend an eternity on the Wall of the Faithless. At this point in time the PC is acting out the wishes of Kelemvor and in fact believes them to be true and just. For now that is his sole purpose. He travels with the party since they were essentially the ones that freed the psychopathic NPC and briefly accepted him as part of their group - he believes their relationship (NPC and party's) is not over and their paths will cross again due to converging goals/meta-plot reasons.
EDIT: Again, this is all the player. As DM I ask and prod to learn more to stay faithful to his backstory.
Cool. That is definitely good stuff! You may well be able to simply get the player to figure out what to confront his own PC with, he seems pretty dedicated to making it an interesting character.
This is all good stuff to bring into the mix. The above stress caused might see the PC act out against the wishes of Kelemvor. Traditional D&D sees me as DM deciding if Kelemvor was offended and if offended, dealing out any consequences. How would that differ in your type of game?
Would you let the die decide if Kelemvor acts out the punishment/consequence?
Oh, it could work out the same way. I would telegraph what is likely at stake. So the PC can make one or the other hard choice, or try to have his cake and eat it too, but only by risking more somehow. In other words, you don't really need, technically, to even roll dice if a player declares a PC action of "let the NPC go so I can save my brother!" The NPC gets away, the brother is saved. There could be checks to see what else happens (injury, brother is only temporarily saved, etc.). Likewise, he could sacrifice the brother and kill the NPC, OK, brother dies, NPC dies, he's made his choice. Of course most players will try to go for the double win, and then let the dice fall where they may! I'd say if the PC fails Kelemvor, then he IS pissed! Maybe this leads to a major turn for the PC, or maybe he just has to redeem himself.
EDIT: This skirts closely to Alignment i guess.

This is similar to @
pemerton's example some years back of Vecna and the imp.
Yeah, Alignment was ideally supposed to be able to help drive this kind of thing. It could work if the players worked it, but then it wasn't REALLY needed. Its an odd mechanic that way.
In one of my previous examples either on this thread or another (I forget), a character handed a magical item to a Frost Giant who had a similar such item (essentially each had a shard of the rod of seven parts). The shards clicked into place and became one item. I ruled the Frost Giant kept such item ignoring the soft protestation by the character (a cough and hand motion to return). There was no die roll. Some posters felt there should have been a die roll.
I'm only asking because if I apply pressures on the relationship between PC and deity it might end up in a situation where fictionally it would make sense for the deity to lash out his annoyance of a decision made by the PC - and essentially I'm asking if you would have it resolved via die roll or DM fiat?
Well, there could be a die roll. I would say that if the check succeeds then the character is on the run, and if it fails, then he's in the soup. Either way there are then further options, maybe if he's captured he gets imprisoned and learns of a plot against Kelemvor, does he go with it and escape, or try to get back in the god's good graces? If he manages to run in the first place, then how does he deal with the falling out, and is he now 'toxic' (IE what about his allies, will Kelemvor constantly go after all of them, unless he heads off alone?). You can go a lot of ways with it, but dice are always a nice option where things can progress in 2 ways and its not really under the PC's full control to choose.