I don’t follow you about breathing being a conviction since breathing is involuntary. When you say going to the wall for the unborn, do you mean prolife against abortion with no exceptions?
Well, yes, involuntary really is not a bad way to describe it. If you have a conviction, that means it is so strong in your mind and heart you would accept any adverse consequence to yourself rather than surrender on the point of contention. I just use breathing as a metaphor to show that a conviction is not viewed as optional by the person who holds it.
As for being against abortion with no exceptions, the court would probably view exceptions as a severe weakening of the conviction. The moral reasoning of the conscientious objector who wins is typically rigorously complete and self-consistent. That’s where the strength of credibility comes from. The judge wants to know that you have thought your conviction through and really own and understand it.
Therefore, if you argue you are against funding abortion because it is murder, but find it acceptable to murder some unborn children because they were conceived through rape or incest, the judge will likely see that as a huge gap in your moral reasoning; you must define your moral objection consistently and apply that definition consistently. If your premise is that protectable human life begins at conception, you will have to defend that premise regardless of the circumstances leading to conception.
Otherwise, your opposition to abortion will begin to look more like a loosely held patchwork of preferences rather than a logically unified and unalterable conviction. If some circumstances make the murder of innocent children acceptable, your conviction is, by definition, not consistent, not unalterable, and therefore not a good candidate for conscientious objection.