Hmmm....
Religious exemption might be easy (there is a legal case, I think, which established that “religion” is bigger than your pastor down at the building with the steeple. It’s not up to him. Also, it goes beyond doctrine. If the Pope is OK with the vaccine, that doesn’t mean every Catholic has to be OK with the vaccine. I think there is a lot of wiggle room on this, and the government (and your employer) is NOT the judge of your theology.