Come on, Tolkien was a devout Catholic and the LOTR is a pretty overt moral "pilgrim's progress" tale in the vein of medieval allegory. I enjoy the books, but I wouldn't exactly say Tolkien worked in any gray areas. The closest it comes to that is Frodo not throwing the ring in.
I think what you complaining about is really that Tolkein wasn't a moral relativist and that shows clearly in his writing.
This is different to the original complaint about a dichotomy - belief that some things are ultimately good and some other things are ultimately evil is not the same as dividing everything into rigid categories of only good or only evil.
Calling it a pilgrim's progress tale is a bit unwarranted, or at least overly reductionist - it's not that simplistic and that's only one aspect of LotR anyway.
A few grey areas off the top of my head: various elven decisions, Denethor, Frodo, Smeagol/Gollum, Saruman's initial study of ringlore. In Tolkien's writing, individuals do clearly good things, clearly bad things, difficult to judge things, and and things that are some combination of the previous three. All this happens within the framework of the very traditional overarching light v. dark theme (which is also the source of the association between evil and 'dark' and 'twisted' characterisations that some like to complain about).
> a devout Catholic and the LOTR is a pretty overt moral "pilgrim's progress" tale in the vein of medieval allegory
It's much more subtle than that. LOTR has characters who are deeply ambiguous, and do not fall clearly into Evil or Good in a traditional sense. Folks like Denethor, Gollum, and even Boromir have multiple facets. Even Frodo is tempted to use the Ring multiple times even though he is aware of the implications.
And let's not forget that, in the book (not the movies, which missed the point of that part completely), the Shire is ultimately destroyed even though Frodo was successful in destroying the Ring. That is clearly not your typical, regular fairy tale ending.
You probably haven't read a line from him if you say this. Do not mistake the author for the movies from Hollywood.