As long as the decision is indeed fully conscientous, then an individual has the right to object to anything. This same principle is directly related to an individual's fifth amendment rights; the right to remain silent. As long as they are fully aware of the outcomes and repercussion from both decisions, an individual has the right to refusal of anything.
There are many reasons why a person may feel the need to use the right to conscientious objection that are very justified. Some may know that they are not able to morally, mentally, or physically be able to perform a duty required of them or to support an injustice. This should be each individual citizens right. This is important to not only the person who wants to use his or her rights to conscientious objection, but also important for the safety of the people who may be negatively effected if the person is not able to use their right of conscientious objection. If they are not able to use this right, they may perform their job in a less than acceptable manner which could put co-worker, family, friends, and civilians at risk.