In both your programmer case and the case of the catholic hospital staff member you have a very clear option, you can not work at that facility. Don't want to write code for military weapons, cool then work somewhere that doesn't do that. Don't want to provide abortions at your work, cool then work in a medical facility that doesn't provide them. Many facilities don't perform abortions just because they aren't intended to, such as clinics etc so you should work there.

Your programmer case also doesn't make sense because extending the metophor you want companies to be allowed to not develop software that is used by the military...they can already do that.