Before I go further, I would like to apologize to everyone, I did not mean to have my example dominate the thread like this.
....sooo....you made a homicidal, anti-social zealot with a self-hate complex? Yeah....I don't see that going over very well with a group if you're going to play him the way you seem to describe, namely kill everyone and let their blood run in the streets. The kind of party that would be fine with that murderhoboing would...well be more murderhobos, and they likely wouldn't bother trying to "redeem" you, or give him some avenue to change. And a group that wouldn't be along the murderhobo alignment probably would look at him like, well, a homicidal maniac.
Also, not really sure how well the "doing the complete opposite of the god I worship" would fly, especially for a god like Sarenrae. I mean it's canon in Pathfinder that she's got a clan of goblins converted to her, you know, because she believes in redemption and stuff. I mean this is a reality where gods are ACTUALLY real, and like manifest and stuff. I suspect that Sarenrae might take issue with someone running around slaughtering in her name, when it's specifically antithetical to what she stands for. Since you implied that he's going around smiting those that don't actually need smiting.
Respectfully, that paragraph makes me think I explained it poorly. I wouldn't necessarily describe the guy a murderhobo, for instance, as unless he has strong reason to believe that a person is willingly involved with the cult of Rovagug he's not going to go out of his way to hurt them. This isn't to say that he won't fight if the situation demands it (he's by no means a pacifist), but he certainly doesn't go around killing people for funsies.
To help explain this, let's look at a few different situations:
1) Zerris finds a bandit mugging a old lady on the road. He goes in to fight the bandit and protect the old lady. Like most adventurers he probably wouldn't shy away from lethal force, but if the bandit cuts and runs and leaves the lady's stuff behind he's not going to give chase. Lady tries to thank him, he'll shy away because...well, it's a familiar song and dance. Lady gets a good look at him, sees what he is, screams that he's a monster...he'll sigh, deflate a bit and walk away a little depressed.
2) Eating in a tavern, some tough guy drunk tries to pick a fight with him? He'll do his damnedest to escape the guy's attention. Drunk keeps insisting, he keeps refusing...guy tears off his hood and all of a sudden all eyes in the tavern are on the 'monster' in the room. For the sake of upping the stakes for the example, we'll assume some yahoo adventurer decides to draw his sword on Zerris. Given the option, he'll drop the coin for his tab on the table and walk out. If not given the choice and the adventurer starts fighting, he'd try to disengage and bolt. He'd be upset about losing a good place to eat and feeling terrible, but that's about the extent of his negative reaction to it. If anything, he actually presumes that they were
right to drive him off and that it's another sin on his shoulders that he needs to repent for.
3) He gets sent after a cult of Rovagug? Guy stakes out the target, looks for evidence corroborating the accusations, figures out who else might be involved, and then gives them no quarter, taking vindictive pleasure in eradicating them.
To try and sum it up, it's probably easiest to think of him as if he were seeking vengeance on Rovagug. If you aren't associated with Rovagug, you're probably no more in danger from him than you are most other adventurers. He'll fight if combat's required, flee if the problem is his presence, and generally will try to stay beneath notice rather than cause trouble. If, however, you
are a willing associate with the Rough Beast, and he verifies it, he's going to try to kill you with the same glee as Hellsing's
Alexander Anderson would. Or to be more classical about it, Rovagug is the White Whale to his Ahab. Much like Ahab he's actually a decent enough sort when 'the whale' isn't involved, but when it is guy sees red and prioritizes hurting it over everything else.
I maintain that the guy takes too much enjoyment in paying evil unto evil and basically loses himself in those moments, but I'd argue that the fact that he only has those moments when Rovagug or his cults are involved makes him more Jack Bauer than murderhobo. Whether or not he's an edgelord...I'm obviously the least qualified to judge, but as I said he's a character I still consider a WIP and I've been very hesitant about him specifically because of such concerns.
As another point of clarification, I would apologize for some poor phrasing on my part. When I said that "he's internalized the common knowledge that - because of what he is - he
can't be good, and he hates himself for it", that should have been that common knowledge is that he can't be good, and he internalized it as meaning that he's naturally evil and has never redeemed himself of the sin of his nature. This accounts in large part for the anger towards Rovagug and glee in eradicating his cults, he thinks that in so doing he's rejecting his nature and proving he can rise above it. Eliminating these cults was the mission the church gave him, and he's misunderstood that to be his penance, with the further misunderstanding that his penance won't be complete (and thus he won't have
earned the goodness he strives for) until such cults no longer exist. He
tries to be good, but he treats goodness as transactional and believes that he'll remain deeply in the red until his mission is complete.
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Edit: I think I just figured out a more succinct way to put it, and that would be by looking at the pantheon. The character is a devout worshiper and desperately wants to do honor to Sarenrae, but his character flaws make him (at introduction) a bad match for for her. Not the worst match, but certainly not a good match. If you were to ask his superiors what god they'd peg him as the best match for and they honestly gave it consideration, they might say Gorum. This isn't actually true, however. Such a conclusion is mostly due to circumstantial evidence filtered through their own prejudices (nobody's perfect, and I figure this would be a
damn hard prejudice to shake even for a Sarenrite) and unwillingness to actually get to know the guy enough to have a good feel for him. In actuality, he'd be a
spectacular match for Ragathiel. You know, tries to prove his goodness, unforgiving to his foes, struggles with his darker impulses, can fall victim to lapses in judgement and going too far in pursuit of punishing the wicked...that's basically Ragathiel's faithful in a nuthshell if not Ragathiel himself. But while that is a better match for the character, he wants to be a good Sarenrite and struggles with it.