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?".
> "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.
If trying to rationalize things - I'd say Sauron knows that giant eagles are a thing, and able to serve as mounts. So to prevent Western aerial reconnaissance and insertion/extraction of observers/spies/special forces in Mordor, he's got to have some sort of aerial observer / aerial denial systems going. Which systems would make a "fly the Ring to the fire" gambit too risky.
(Vs. voice-of-canon Gandalf makes it clear that anyone seeking to destroy his Preciousss is simply beyond Sauron's Vile McEvil worldview.)
In fact, when Gandalf catches up with Aragorn/Legolas/Gimli in 'The White Rider' chapter, he explicitly tells them that Sauron has committed a major strategic blunder: attacking too early, as soon as he thought the Ring was in play. If he'd kept some forces back to guard Mt Doom, he'd have been alright. Especially because, as later becomes clear, Mt Doom isn't a normal volcano where you could just lob the Ring in from your low-flying eagle. The Cracks of Doom are in a chamber deep inside the mountain.
Speaking of things needing rationalization: Smelting iron, which the dwarves are supposedly past masters of, requires furnaces which routinely exceed 1,500 °C. Vs. even exceptionally hot lavas are considerably colder. So why bother forming a Fellowship of the Ring, or embarking on a long & dangerous journey to Mt. Doom, when it'd be vastly quicker & easier to smelt local?
Mount Doom is magical/mythic in nature, the birthplace of the One Ring, while the Dwarven forges aren't.
Quoting Elrond during the Council at Rivendell:
> “It has been said that Dragon-fire might melt and consume the Rings of Power, but there is not now any dragon left on earth in which the old fire is hot enough; nor was there ever any fire, save the fire of Orodruin, that could melt the One Ring.”
Also, the Dwarves that took the One Ring for melting would have likely fallen under its influence, postponing the destruction and ultimately keeping the ring as a keepsake, tool or weapon, like most living creatures would... except for some brave Hobbits, which took a longer time to be corrupted.
More fundamentally, this is not the kind of mindset with which Tolkien wanted us to read LotR. It can be done for fun, but if done seriously, it'd be missing the point.
Note I wasn't really trying to go into the argument, just pointing out these are well-known and very debated topics in Tolkien fandom.
My own opinion is that debating this is missing the point. Tolkien was about the hero's journey, which necessitates the hard path to victory. It's not at all about flying a modern superweapon into Mount Doom; that's too literal a reading.
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
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?".