There’s an interesting case right now in Vancouver against the largest hospital downtown which is affiliated with Catholics (I think, St Paul’s is the facility in any case).
Several in-patients that opted for medical assistance in dying were refused that treatment by administrators of the hospital on religious grounds, and their families are sueing based on the additional suffering inflicted by having to transfer to other facilities.
If your job duties might go against your religious beliefs, you are responsible for finding other work. Not doing so should be grounds for termination.
In general in the US only White Evangelical Protestants and Black Protestants have less than a majority who believe assisted suicide / euthanasia should be available for "great pain and no hope of improvement", and those two groups still have over 40% who believe it should be available.