A Simple Task of Providing Support from the Shadows to Defeat the Demon Lord/Defeating the Demon Lord's a Cinch (If You've Got a Ringer)
If I were to generalize this series and put it into one of the generic isekai subcategories, then I guess it would technically be under the "crucial party member for defeating the demon lord gets kicked out", I guess. Technically. The art's a bit rough, the translation a bit scuffed, but I like it. This manga is adapted from a LN.
I'd say this series has some similarities to The Misfortune of Local Knight Hans, the main character is a native in a fantasy world that has to tardwrangle the living idiotball of an isekai'd hero. Actually, you could say that everyone is holding on to a bit of an idiot ball here, but I guess there are reasons for it.
Anyway, as mentioned earlier, the premise is that an isekai'd Hero is summoned by the Holy Church to defeat the Demon Lord, and a party is created to assist the Hero, one of whose members are the MC, Ars Crown. He's given a mission to help the Hero defeat the Demon Lord, whose starting party consists of the low level lawful stupid hero, a low level mage that can only use fire magic, a low level swordsman that can't use MP at all, and him, a highpriest that's basically an Executor from the Burial Agency. Guess who eventually gets kicked out? Though to be fair, MC does do various things which might be deserving of it, and some things definitely not.
After MC gets kicked out though, he reports back to the Church and gets told that his mission isn't "Defeat the Demon Lord as the Hero's party member", just "Help the Hero defeat the Demon Lord", so starts his real quest of trying to aid the Hero's party in the shadows.
The world setting is relatively generic manga fantasy with a Demon Lord, with some variations. EXP is basically a thing, as a blessing from God, humans can absorb parts of the soul of things they kill, which will strengthen them and level them up, key point is things they kill, so there's no EXP sharing. There's what appear to be adventurers, but they're just called what they really are, mercenaries. There doesn't seem to be a guild for them either. There was a tavern where mercenaries gathered and took missions, but it just seems to be that, a tavern where they gathered for convenience. There is precedent for hero summoning, but I don't know how many they've summoned over the course of history, but it seems like there's only one active hero at the moment, possibly only one active hero at a time allowed by God.
For the MC getting kicked out of the party, while not directly stated, the main reason was probably because he's not female. The Hero only wanted female party members, and the male MC showing up instead was unexpected.
The second reason, was probably because he was causing a lot of discord in the party by being very vocally upset at how underqualified the other two party members were. The average level in the party excluding him is 15 at the start. A party with average level 80 got decimated when they went to fight the Demon Lord. MC estimates they have about 30 days to powerlevel the Hero to a level where they can at least run away from a Demon, because that's about how long the Church suspects it will take for the Demon Lord to realize a Hero has been summoned and send someone/something to find and assassinate them. And since there's no EXP share, the idea of having to powerlevel two other deadweights are... bad.
The third reason, despite being very helpful during his time in the party, MC's conduct is very unpriestly and very, very obviously lies about what level he is at the beginning. Probably the MC's biggest idiotball bit, though it can be debated, is that he spent the entirety of the time in the party trying to avoid letting the Hero realize how relatively weak their entire party is.
1. So this gets revealed around the recently TL'd manga chapters, and you'll probably assume this pretty quickly, but the Hero is actually a girl. All previously summoned heroes have been male to the point that nobody has thought that the Hero could be female, and even the divine equipment bestowed to the Hero assumes they'll be male. She also seems to have androphobia, physical contact with men is pretty unsettling to her. For some reason, MC hasn't been informed and hasn't realized.
2. They actually seem to have very high potential, but the other reason for sending immature young girls to the Hero's party is suspected to be a honeytrap, since taking the Hero's bloodline is what people have done the previous times a Hero was summoned.
3. MC thinks the Hero is mentally unstable, and they have had a minor breakdown in front of him near the start, where he basically tells her if she dies, the entire human world dies with her. But as a result, the MC definitely treats the Hero with kid gloves in how he constantly tries to avoid letting them realize how weak they are, as mentioned before.
MC is unpriestly, and constantly gets compared to a sister that the Hero met at the start of her journey about how he seems to keep breaking their commandments. I think the Hero being isekai'd also leads to her thinking about the tropes of corrupt shady priests, but as far as I can tell, that really isn't a thing in this world due to the Gods directly being the basis for holy powers, and the MC is very devout.