Medical facilities, like bakeries, serve the public. When you work for either one, you park your car, and your religious beliefs, outside, and do the job you have agreed to do when you entered into an employment contract. Don't want to bake wedding cakes for LGBT couples? Then don't work in a bakery. Don't want to perform sexual transition procedures? Then don't work in that aspect of medicine. (I hear respiratory therapists are in demand atm...).
When you go to Burger King, does the counter person who is Hindu or Buddhist or 7th Day Adventist refuse to make you a Whopper because of their religion?