If their beliefs get in the way, they need to find another profession. This is pretty well established across the entire industry.
You must provide the same level of care for a pregnant teen, a smoker dying of lung cancer, or a neo Nazi. It doesn’t matter how their lifestyle offends you.
You’re absolutely right. Such procedures should be treated the same, as much as is appropriate. (vasectomies are a much more minor procedure, so things like recovery support would be different)