Actually, the concept of a just war does involve conscientious objection nowadays, since most modern wars are unjust, in one way or another. Catholics in 1941 said it is a matter for individual consciences to ascertain whether the war being fought is just or unjust, and other factors influencing it, and if conscientious objection is the right decision or no.
I was actually referring to the legal criteria by which one could be classified as a non-combatant, and therefore exempt from military service, by the US government. Per 401 US 437, Gillette v. United States, the majority opinion by the Supreme Court held:
'The exemption for those who oppose "participation in war in any form" applies to those who oppose participating in all war and not to those who object to participation in a particular war only, even if the latter objection is religious in character.'
More specifically:
'It should be emphasized that our cases explicating the "religious training and belief" clause of § 6(j), or cognate clauses of predecessor provisions, are not relevant to the present issue. The question here is not whether these petitioners' beliefs concerning war are "religious" in nature. Thus, petitioners' reliance on United States v. Seeger, 380 U. S. 163, and Welsh v. United States, 398 U. S. 333, is misplaced. Nor do we decide that conscientious objection to a particular war necessarily falls within § 6(j)'s expressly excluded class [Footnote 13] of "essentially political, sociological, or philosophical views, or a merely personal moral code." Rather, we hold that Congress intended to exempt persons who oppose participating in all war -- "participation in war in any form" -- and that persons who object solely to participation in a particular war are not within the purview of the exempting section, even though the latter objection may have such roots in a claimant's conscience and personality that it is "religious" in character.'
My point was simply that there would be no appeal to CO status, unless one objected to all war. Since Catholic dogma does make allowance for morally just warfare, a Catholic could not truthfully gain CO status on religious grounds.