Yes, Tolkien had his opinions about life in the world he knew, but to say he had an "agenda" is a bit bold.
I mostly agree with you, but this, you contradict yourself later in your post.
It was at the least an essay on how he thought the world should be.
That's an extremely political project. As you say, it's impossible for an author to keep opinions out of her work, but any time you're saying "this is how the world should be" or "this is how the world shouldn't be" or even (and Tolkien does this explicitly) "this is something that's wrong with the world as it is," you're engaged in a specific, political critique. When you're telling the audience, even in story form, what you think the world should ideally be, you are, yes, preaching and yes, you have an agenda.
And in the end, all fiction is political. All authors have an agenda. Every single one. Some may get their views across more or less painlessly, or more or less recognizably. But just because you don't notice the agenda doesn't mean it's not there. It just so happens that Tolkien couches his agenda in terms that are easily swallowed by a lot of people.
Now, that's not to say that one of his major aims wasn't to tell a cracking good story. Sure, absolutely it was. But there's politics all through that story, and it's not an accident.
Nor do I think Mieville was overthinking it. I don't entirely agree with his assessment on all points. I certainly can't get too upset about Tolkien's attachment to Catholicism--I don't practice, but I was raised Catholic, so that all seems homey and familiar to me more than anything else. But the images we take from narrative, and the implications of those images, do shape our thinking.
For instance. thedreameater's original post (and, yes, thedreameater is one hundred percent entitled to their opinion of Tolkien and Mieville, no question) is shot through with a very medieval image of how readers and writers should ideally relate to Tolkien. Tolkien is the king, no one should question him. Even if you disagree, or dislike, one must bend the knee to the king.
That's really interesting to me because I assume that thedreameater is the citizen of a republic or a democracy, so why would they conceptualize relationships in that framework? It's not democratic in the least, is in fact vehemently anti-democratic. And yet it's shaping their view of how relationships should ideally be, at least in this venue, the land of writers and readers.
I don't think Tolkien was or is evil, but I do think it's worth considering just what we take away from stories that we assume aren't political, aren't preaching, don't have an agenda. Often, those are the stories that have the biggest impact on how we conceptualize situations and relationships in the real world, in our lives, because we accept those frameworks without questioning them.
I think he would be disappointed if his work was viewed as a political/religious statement. In fact, he hated allegory, which was one of his biggest critiques of Lewis' TCoN.
Allegory is not the only way to make a political or religious statement. It's merely one of the most ham-handed, unimaginative ways. Tolkien didn't dislike allegory because it was making a statement, he disliked it because it was unsubtle and insulted the intelligence of the reader. If I recall correctly, that is, it's been a while since I read his actual words on the subject, but that's what I've come away with.
Tolkien's work is not
only a political or religious statement, but political and religious statement it is.