So here's my issue: I like my character, I like our party, and I don't want to pull a 180 on my character and make him nice or throw away important motivations for him.
Well, it sounds like your character just may be evil, or at least on the evil side of neutral.
That doesn't mean he has to do evil things, especially if he has a reason not to.
And, if he wants to stay with the party, he probably does. You've already had an in-character conflict where one character "stormed out" and another "left the room disgusted." That ought to be a pretty good clue to your character that, if he wants to hang around with these guys, he'd better start to act nice, even if he's only doing it to keep the other party members cooperative.
Even if your character was a complete psychopath who loved kicking puppies, if he was sufficiently smart he should be able to realize that there are situations where it's better to heroically save the puppies instead. And it doesn't sound like your character is anywhere near that bad.
Basically, you're playing a conflicted character. This can be a lot of fun, if that's the kind of thing you like.
It doesn't matter that the cause of the conflict may be (at least initially) external; even so, it's a source of mental conflict for your character. On one hand, your character worships an evil god. Even if his choice is fundamentally based on pragmatic reasons (power!), a pact with Cthulhu will surely have some influence on him, tempting him to more evil acts and means (not that a hunger for power couldn't do that all by itself). On the other hand, he's also fighting to save the world (even if it might be for his own ends), and has teamed up with a bunch of more noble, good and squeamish types to do so. This means that, whatever means he might want to employ in the pursuit of his goals, he now also has to consider their effect on his fellow party members.
And, of course, once he starts to consider the way his actions are perceived by others, he might also gradually come to realize that there's also a side to himself that doesn't like what he's doing. Maybe not instantly, but after a while. Morality has a funny way of growing on you like that — from "I have to be nice or I'll get punished" to "hey, other people are actually nicer to me if I don't act like an asshole" to "you know, I really should be nice just on principle, because it makes the world a better place."
None of this means "pulling a 180" on your character, or at least, not in a way that he wouldn't have good in-character reasons for. Sure, the conflict with the other party members (and possibly subsequent reflection) might be the trigger that makes your character realize that he needs to drastically change his behavior in order to achieve his goals, but his motivations will still be the same as before.
My question: Is this possible?
Yes, it's possible, whether or not the fiend and the god/goddess get along. There is no RAW prohibition from the multiclass, no matter how awkward it looks.
From a purely RAW standpoint, I don't think that Warlocks can lose their powers, but would his good deity even bother with someone who sold their soul to a devil?
This depends on how the DM plays out the deity's and the fiend's role. Points to raise as you two flesh this out (a collaborative effort between you and the DM):
- How much of a role does redemption play, a deity accepting a lost/troubled soul (bound to a devil) into the fold? The Sword Coast Adevnturer's guide supplement for D&D 5e has some material on FR deities; Baervan gets one sentence of treatment (p. 115) and Chauntea gets a few paragraphs( p. 27). For more detail, you could back up this guidance for Chauntea or Baervan with previously published material and make your case to the DM for why, or why not, either deity fits. Deities thrive on having followers.
Playing an internally conflicted character is rich with role playing possibility. Trying to serve the good, still dealing with evil ... that's a standard story IRL, and an element of stories from many different cultures. This would allow the link with the Pit Fiend to remain -- but there's always a price to be paid! (This could provide DM some fun, occasionally at your expense! :) )
And would that pit fiend continue fueling their powers?
Why not? Here's a point of view that the Pit Fiend could take:
"I've got my hooks into this gnome, I won't let him go. So he wants to get in with that goddess/god? Good! I can use him to cause trouble for (chosen deity), and then enjoy his suffering as he realizes that it's his fault -- due to his hunger for the power only I can give him. Muahahahahaahaa!"
or
"I don't like (deity), but we both have (unrelated) unfinished business with that #@!^%$ Orcus, and this gnome will serve nicely as a proxy. In the end, I profit! Muahahahaahaa!"
You and the DM should be able to work out a deal, and some tension, that fits the campaign.
One last point to address as you work with your DM on this multiclass:
How important is alignment in this campaign?
Alignment in 5e is a bit different than in previous editions. It is more like an ideal for the character, and a matter of how the player should behave. How well the player character lives up to it, and what the rewards/penalties are, lay in the realm of DM's discretion.
With that in mind, and the two deities to choose from: Chauntea's clerics appear to require a serious commitment, and a decision on being a Pastoral or a True Shaper (the latter looks like a better fit for an adventurer), while Baervan's yoke looks like it is lighter to bear for an adventuring cleric.
Could the pit fiend and the god/goddess get along?
That would require a serious threat that both of them want to counter, something opposed to them both for different reasons ... so that you would be serving both of their interests (roughly) at the same time. Some existential threat to the world itself ... that too lies in the realm of how your DM is running and shaping the campaign.
Best Answer
Any character can worship a god, but only certain classes actually benefit from it in terms of game mechanics
Appendix B: Gods of the Multiverse (from the basic rules or PHB) describes that people may worship any god... or even multiple gods.
If you want to be a "servant of your god", that's perfectly fine. The Acolyte background models this quite well, without affecting which class you choose. So long as you aren't thinking of gaining magic through your worship, then any character you create can be a servant of one or more gods.
Receiving spells from your god is modelled by specific classes
However, when you start talking about spells, that's where the "class restrictions" come into things. Although your DM may be imposing different rules depending on their setting, generally speaking, if you want to get spells from a god, that means being a cleric:
Paladins may also gain their powers from a god, although paladins in 5e aren't tied to gods as much as in previous editions:
Warlocks aren't as clean cut; generally, warlocks make a deal, a pact, with an "otherworldly entity". Whilst your DM could decide that such a being is a god, generally the implication is that it's another sort of powerful being, such as a archdevil, an archfey, an angel, etc.
Finally, I will also mention druids and rangers, who also gain magic from "divine" sources (the distinction between divine vs. arcane magic isn't really as much of a thing in 5e, but many D&D players use those terms), although they may also get their magic from "nature itself", so they don't strictly need a god like clerics do:
In your case specifically, I'd recommend rogue with the Acolyte background
Based on the part of your question that says:
If you picked the Acolyte background, as I mentioned above, this would give you that "servant of the gods" flavour but without clashing with your class choice of rogue, and if you let your DM know that you aren't expecting to get any divine magic out of this, it's just for flavour, hopefully he should be fine with that.
As a rogue, you get something called Expertise at 1st level. You are allowed to add your proficiency bonus twice instead of once to any two skills you are proficient in. If you make sure that you pick Stealth and Sleight of Hand as two of the skills you are proficient with (rogues are allowed to pick four from a subset of skills, as explained here; these four plus the two you get from the Acolyte background should see you with a total of 6 skill proficiencies at 1st level), then you can pick those two skills as your "Expertise" skills.
It's not quite advantage, but you will still be extra-good at Stealth and Sleight of Hand because of it, and you can still flavour it as "guidance from the Crow Lord", even though in terms of the game mechanics, it's just your rogue's base class feature and nothing to do with the gods at all (which should hopefully keep your DM happy).