We should expand the definition of conscientious objection- it shouldn't be limited solely to people who oppose ALL wars, but instead- as the 1968 Democratic presidential peace candidate, Eugene McCarthy argued, be extended to those who conscientiously object to particular wars- this would have meant, in that era if, that a person could get conscientious objector status for Vietnam/Cambodia if they had specific moral objections to that conflict, but would gladly have fought in World War II or on the Union side in the Civil War. There's no reason a person should be forced to demonstrate that the oppose ALL wars that have ever been fought.
There is no reason that we shouldn't say it's valid to support one war but refuse ono moral grounds to serve in another. Not all wars are alike.