I think it is pretty clear - Kelemvor is turning a blind eye to the whole thing as long as it doesn't cause too much chaos in the city. That's why he was letting the crusade go the way it did, why he lets Kaelyn get away with raids on the wall. Hell, he openly admits the injustice of the wall, only stating that it is necessary to avoid the greater evil (that being the gods throwing a fit for losing worshipers - he outright states it so).
And he isn't the only god to do so - Kaelyn is an active cleric of Ilmatter after all. I think it is safe to say that a significant opposition to the wall could exist among the good aligned gods.
Actually, he stated that he found the punishment met out to Akachi and by extension the PC is unjust. That is because Myrkul went AGAINST what the Wall was for to punish Akachi. Remember, you need to be an atheist to be stuck in the wall. Akachi wasn't. Sure, he betrayed Myrkul, but that made him a False, not a Faithless. A False wasn't supposed to be stuck in the Wall. That is why he turned a blind eye to it... THIS time.
On top of that, Myrkul ripped him out of the Wall in order to create the spirit eater curse to begin with. That, again, wasn't supposed to happen. In fact, the only other time we know it happened was when Cyric had Gwydion taken out of the wall before he got really eaten in order to be made into one of his clockwork knights. That didn't end well for Cyric either.
Kaelyn being an active cleric of Ilmater is something that I profoundly disagree with. I stated as much before here in this forum.
Regardless of what kind of retcon they did in order to make the Wall what it is, it is there to serve a purpose in the Realms. In the context of the Realms, it is there as the equivalent of Hell. Remember that in the Realms, EVERYONE goes to Paradise, or rather their version of Paradise. Even a worshipper of an Evil god goes to "heaven". So what happens to those that has no gods, and in fact has nothing but spite for all the gods? They had to go somewhere. That is the Wall. It is a removal of the presence of all gods, i.e., non-existence, something that those who are versed in the Christian doctrines would be familiar with.
Going against that basic foundation of the cosmology of the Realms should be profoundly against ALL clerical beliefs and teachings. It is like Christians thinking that Hell should not exist, that it is so profane and Evil that whoever that created it (or allowed it to be created) should be reviled, and that all people sent to Hell must be saved by pulling them out of Hell. And given what Christians believe about God... well, you draw the lines.
Whether Kelemvor agrees with it or not, it is his DUTY to look after the Wall. He has reasons to not meddle and wear that mask of his (namely the last time he tried to meddle in "injustice", it basically required Ao to sort things out, and Ao was NOT happy to have to interfere). So, yes, as a Lawful Neutral deity, he had no choice but to obliterate Kaelyn. Now, being a pretty nice guy (he was actually practically forced into taking up a LN alignment; he was originally closer to LG, IIRC), he would have given Kaelyn warnings and plenty of chances, but in the end, he would have to act, regardless of whether he liked it or not. That is his duty.