I have no problems with religious hospitals and hospices, filled with great people doing great work.

But you only have to glance briefly at history to see numerous examples of these wonderful institutions inflicting and prolonging horrific pain and suffering on their patients because 'it is God's will'. 
 
Religion fought antibiotics tooth and nail, pushed hard against insulin, and many are still trying to stop vaccines of all types. Think of the lengthy and still ongoing religious fight against women's health. Remember when Catholic bishops went on TV telling parents it was a sin to give their girls the cancer-fighting HPV vaccine - that wasn't a one-off. In lots of countries religion fights to keep abortion illegal even when the woman's life is in jeopardy.  

History has taught us that taking religion out of medicine makes our hospitals more ethical, not less. And the less say my priest has on my end-of-life decisions, frankly the more right my decision will be for me.