Accuracy based on how you think it should be? Or accuracy based on how Tolkien meant for it to be? You're trying to argue historical accuracy about a series of books that is not based on history.
Can you explain why you have re imagined this as a debate on realism, then?
I am talking about accuracy based on fidelity to how Tolkien fleshed out his invented world. His books evidently are not a historical adaptation (I really fail to see why I have to point this out), but the cultures contained within and some of the figurative events and personalities involved with those cultures are most often either lifted from history or historical literature. The Rohirrim are not "loosely based on North European cultures", they are the Anglo-Saxons of Mercia given cavalry and Saruman for neighbours. Their language and their names are Old English. In a letter, Tolkien said that their clothing should be based on that of the Anglo-Saxons in the Bayeux tapestry. The "Mark", their homeland, is a phonetic spelling of the name "Mercia" in the Mercian dialectical vernacular. Read Tom Shippey on this- he covers it all at much greater length than I can.
Despite popular belief that all of Tolkien's ideas are original and malleable, he often reprocessed concepts found in early medieval history and literature. The magic rings and the Dwarves are lifted from the
nibelungenlied, while the Dwarves' names come from
Edda. The dragon with it's hoard of treasure comes directly from
Beowulf. "Saruman" is "wily man" in Old English. "Gandalf" is "elf with staff" in Old Norse. Tolkien's truly original creations are the Hobbits, and the Orcs, though the material culture and language of the latter seems to be highly Turkic.
Now, all of this doesn't mean that you can't give the Dwarves a funky axe design just because it looks funky. But Weta took immense care to understand the roots of each imaginary culture, which makes the faintly African Dwarven axes seem like a rare misstep.
It's not a massive issue, but I would fix it if it was up to me. I am astonished that this is such a controversial viewpoint!