Where to start…
First, it is not always or necessarily wrong for women to wage war. St. Joan of Arc led military forces and placed cannon, although she did not personally wield weapons. Matilda of Tuscany, who has her status in St. Peter’s, did both lead and fight. And there are a fair number of cloistered nuns who have had to use polearms and axes to protect their chastity and their lives.
In general, women fighters have been fighters of last resort, defending the home. And in general, the Church has tried to make women and children off-limits for war, with women and children staying noncombatants in exchange for protection. But against bandits, outlaws, murderers, and other threats to home and homeland, Catholic women have often picked up guns or other weapons. We have a right and an obligation. We also have the biblical examples of Ss. Deborah, Jael, Judith, etc. And Mary has always been viewed as an all-conquering general when we need her most – one of her titles in Greek is Hypermachos Strategos.
Moving along to Eowyn – Lord of the Rings is Catholic, but it tells of a pre-Christian revelation world. Eowyn, as she tells you herself in the book, is a shieldmaiden. In various pagan Germanic and Norse societies, girls were taught weaponry for defense. Some of them spent their younger years as fighters,often because of a man shortage; they were called shieldmaids. There are various sagas and poems about such women. (There were also Norsewomen who took.on the legal status of Norsemen for all their lives, typically for revenge or inheritance reasons. But those weren’t shieldmaids.) One of the darker portrayals of a shieldmaid was a girl who called up her father’s ghost from his barrow and demanded the cursed sword Tyrfing from him, even though it had been his death, so that she could avenge him. Which she did, and founded a Norse dynasty too. But obviously being a shieldmaid did not work out for Brunhilde. And so on.
Eowyn, like Theoden and Eomer, are characters from the primordial past of the Germans and Norse, when they were horse nomads off the steppe. They deal with things like going fell, ofermod, oathkeeping, and snippets of Old English poetry. It’s great stuff. It is Catholic because it is lore. It shows the glory and the tragedy of the pagan world, and it hints at our redemption by Jesus still to come.
Eowyn is Eowyn. The courage is good, the suffering is sad, the hero worship is confused with love, the recklessness is stupid, the PTSD is realistic, and the way she turns away from futility toward life and love is beautiful.
(Technically, most people in Middle Earth are monotheistic, because Numenor was monotheistic. But some of the fictional Middle Earth relates to historical cultures, and speculation about them. Mostly Rohan, because Old English was Tolkien’s scholarly field.)