> they tap you for a conflict which you have ideological differences with, YOU ARE GOING irrespective of your convictions

Your statement is not entirely true, it is not irrespective of convictions. A conscientious objector is defined as either:

A member who, by reason of conscientious objection, sincerely objects to participation in military service of any kind in war in any form.

or

A member who, by reason of conscientious objection, sincerely objects to participation as a combatant in war in any form, but whose convictions are such as to permit military service in a noncombatant status. Also referred to as noncombatant duties or noncombatant service.

Yes there is an application which can be denied. Here is a GAO report on the rates of that. In an all volunteer force the numbers requested are pretty small.

Text version: https://www.gao.gov/assets/a267698.html PDF version: https://www.gao.gov/assets/gao-07-1196.pdf

I think you're being deliberately obtuse as to the parent poster's point. In 2003 the military was abused to start an illegal war that many knew from the start was wrong and had ideological objections. The Iraq war had a grievous effect on morale and on our moral standing in the world. Most of us are quite willing to defend our country by force, the question is how to avoid being sent into another pet project like that. If we want the military to be respected and prestigious, we need more robust protections against what happened in 2003.