Your criticism of Catholicism is valid, but regardless: this dilemma of Tolkien is real, and well-documented (e.g. in his letters, etc).
He really did struggle with this, re: the origin of the Orcs, whether they had souls, whether it was ok to default to massacring them without second thought, etc. He never really resolved it.
Most Tolkien fan communities are aware of this dilemma, it's one of those well-known things, along with "did Balrogs have wings?", "couldn't they just fly to Mount Doom and drop the ring?" and "why did Sauron need to put his power within a ring, anyway?".
Yes - I am not saying that JRRT himself was anything less than saintly, or did not struggle with the issue.
My issue is with the Wikipedia article's heavy identification of JRRT's personal dilemma with the Roman Church and its doctrines. Historically, for that Church - one could just assume that the orcs were Protestants, so slaughtering them was perfectly okay. https://en.wikipedia.org/wiki/French_Wars_of_Religion
> "couldn't they just fly to Mount Doom and drop the ring?"
If the allies were counterfactually sensible enough to fly the ring to Mordor, Sauron could have been counterfactually sensible enough to station an Orc/Troll Battlegroup at the Sammath Naur, with a Nazgul combat air patrol.