What is a person who refuses military service on the basis of religion called?

A person who refuses military service due to religion is called a conscientious objector. Conscientious objection existed before the ratification of the United States Constitution, allowing people to follow their beliefs even during a draft.

The U.S. Department of Defense defines a conscientious objector as someone who has a "firm, fixed and sincere objection to participation in war in any form or the bearing of arms, by reason of religious training and/or beliefs." If someone in the military has a change in their personal beliefs or religion and becomes a conscientious objector, it may be possible to receive a discharge from the remainder of their service by going through the appropriate channels.