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While Cardinal George compares it to the conscientious objection that Americans can make towards military service, that is not the case. It is similar to selective conscientious objection, which states that a person already in the military should be able to decide to fight only in just wars. While this is official Catholic teaching, the bishops are not pressing for this. A true comparision to regular conscientious objection would mean that people have the right not to enter the medical field.
In truth, I do not have a major problem with medical conscientious objection, I think it is basically a good thing. My concern is that the U.S. bishops have basically made the seemless garment cover fertility to birth and then skip to one's death bed. They have all this other teaching on economic rights, selective conscientious objection for military service, etc., but they have become a one issue religion. It's as if the U.S. bishops read John 3:16 as: "For God so loved the world that he gave his one and only Son, that anyone against abortion who believes in him shall not perish but have eternal life."
A Faithful Catholic