I must be looking at the wrong articles because the two I started reading were all about logistics. (For both universes.)
My memory of Lord of the Rings is that the Shire mostly makes sense, but outside of the Shire, the world doesn't totally add up. The Roharim seem like romanticized Ango-Saxon eorls, but basically on grass plains and without obvious agriculture, the elves kind of just magically subsist, Orthanc is populated with orcs going through a secret industrial revolution without a food supply, large stretches of the world are basically empty... Once out of the Shire I don't really remember there being serfs or peasants or churches or much agriculture. It's possible my memory is betraying me, though.
That said my view on why there's a perception of Game of Thrones as more realistic than "most fantasy" is that in the 1200s through 1600s there really was a ton of plotting and power seeking, and a ton of violence, and social status really was a huge determinant of who could do what and how much would be overlooked. And lots of fantasy pre GoTs had various kinds of chosen one narratives, with side of light overcoming obvious evil, with middle ages trappings being little more than window dressing on permutations of Luke Skywalker or just sort of pre modern alternative societies. While GoTs goes hard on the violence, corruption, actual class differences, and power struggle plotting, and mostly does so without basing those things on magical or spiritual alignments. So IMO it's got flaws and is not a fantasy retelling of the real middle ages, but just clears a low bar of not really romanticizing feudalism and having power struggles that are more people-driven.
I do think Tolkien is much more influenced by and matches way more pre-1200s stuff. And particularly things like the Hobbit, his outside LoTR writings, fit super well into what I'd label kind of the "Beowulf to Egil" sort of era/time period.
I do agree that the relationship of religion and behavior in the middle ages is very hard to understand from a modern perspective - and I don't think it's some GoTs even tries at. (Though obviously we did eventually get the reformation because the divide between the Bible and the Church grew too large and too obvious, but it's also not very likely the case that those precipitating the reformation disbelieved.)