I've been playing Pathfinder with friends for about a year and a half now, and I tell other friends that haven't played D&D how much I enjoy it. I piqued their interest in the game and offered to DM for them.
I have two new players that are engaging in my NPCs and combat very well! However, I have a player who's playing a Cleric, and tells me that killing people is against his religion, which I understand but, he has spells do damage to people and he requested a weapon.
Problem
I prompted to my players an organization that will help them get around my homebrew world easier and allow them to easily get quests, like bounty hunting, dungeoneering, city protection, etc. It would also allow me to easily generate story, but my players just aren't interested. The cleric isn't interested because he fears the organization's bounty hunting will go against his character's religion. I'm afraid that my player's religious background is going to affect future ideas of mine, and I'm not sure how to work around it.
How do I work around players whose backstory goes against the story?
Background
My prep for the game was mostly the mechanics of the game, how to roll dice and make a character and create a proper character sheet. I went over the backstories with my players a week before we started. My other player, a monk, said he had no backstory and that I could work with whatever. He isn't a huge issue. The cleric explained his backstory and why he became a cleric, but didn't clarify he would be a pacifist.
Best Answer
Get on the same page
Your literal question asks about problems with one specific character background, but you later suggest several of your players are expressing a lack of interest in the plot.
If there is a lack of interest, especially from several players, it may help to step back and have a group conversation about the type of game you want. Once you have explicit acceptance, or better yet enthusiastic buy-in, the lack of interest and any problem that is originating from a subtle lack of interest, is likely to fade.
Make requirements for a new character
As the GM/DM it is perfectly reasonable to put restrictions on the backstory of characters, especially if you make them clear before character creation.
I frequently start new campaigns with a quest giver that will provide the initial quest for the characters and I require the PCs to establish some sort of relationship with the quest giver in their backstory that would make it reasonable for the quest giver to demand an initial favor immediately.
Your case is slightly different, but if you want to center your campaign around an bounty hunting organization it is quite reasonable to demand that the players create characters that are willing and able to be bounty hunters.
Reasonable self-imposed character restrictions can create interesting drama
Sometimes it helps to let there be some tension between the character concept and the premise of the game. That can help create drama.
In your particular case, a bounty hunter that refuses to kill could be interesting. There are bounty hunters in real world America right now and they very rarely kill and can only justify it with reasonable self-defense/defense of others when they do. Obviously, in a DnD type-setting many more bounties will be of the "dead or alive" kind, but even then a completely non-lethal bounty hunter could work if it is built with subdual in mind. Or perhaps it is a support character who helps out the others that are more willing to use lethal options when appropriate. It could also be interesting to see how far they can be pushed before they start compromising that religious code more.
As an anecdote, I played a completely non-lethal elemental adept in Shadowrun for a while. It created some tension, but it worked out because my character was tightly optimized on subduing and supporting spells and didn't object too much when the others killed during the missions.
Of course, such restrictions should be cleared with the GM and possibly even the other players, first for best result. A certain amount of tension between character and premise, handled in a way that doesn't keep the spotlight on only that one character too much, can add drama and aid in fun. A complete mis-match between the two or a restriction that keeps the other players out of the spotlight is a real problem.