Of course you have to choose between your religious convictions and your job. If you are a member of one of the Christian denominations that is pacifist, such as the Mennonites, then you will likely have to make a choice between being a soldier and a Mennonite. Or between being a police officer, and a Mennotite. If you suddenly became a Christian, it seems improbable that you would chose to keep your job that of prostitute, even if the brothel happens to be in one of the counties in Nevada where prostitution is legal. Nor would it seem quite right to insist that the brothel retain you on the payroll as you refused to give your services. A Jewish person who feels uncomfortable preparing pork should probably not take a job in a restaurant that serves bacon and eggs.
The Los Angeles Dodger pitcher Sandy Koufax was Jewish and he decided not to pitch Game 1 of the 1965 World Series because it fell on Yom Kippur. Eric Liddell, made famous in the Academy Award winning movie, Chariots of Fire, would not participate in any races on Sunday because doing so violated his conscience as a Christian; he knew this jeopardized his participation in the 1924 Olympics in Paris, but he was willing to make the sacrifice.
So I have a problem with how Kim Davis who didn’t want to give marriage licenses to gay couples because of her convictions on the issue handled her situation. My opinion is that if she believed granting marriage licenses to gay couples violated her conscience, then she should have done what any conscientious objector does when faced with that kind of problem: resign. It’s what generals and politicians and ordinary people do when called upon by their bosses to do what they think is wrong.
People make choices. If your conscience is bothered, then don’t take the job in the first place, or if you develop a conscience, then be good enough to quit if your conscience is that important to you.
Likewise, if you are a Baptist, then going to a Catholic church and demanding to take communion would be weird. Asking that the local mosque allow you to hand out New Testaments during a call to prayer would be insane. Why would you go to baker you know to be a devout Mennonite and ask her to bake you a cake to celebrate your induction into the Marine Corps? I would not likely allow an atheist an opportunity after Sunday morning service to give a rebuttal to my sermon. Would he be right to sue me and the church for violating his first amendment rights? I doubt it. And I’m not going to go to a Jewish deli and ask for a ham and cheese sandwich, nor would I consider suing them because they refused to serve me. Being a jerk and acting stupid and rude may be something you can do and perhaps it’s even your right. But really? Why would you want to be that sort of person?