That said, some things in both - the fact that all non-white people in Middle Earth are under Sauron's thrall, for instance - makes me quite uncomfortable. And seeing the very few scenes featuring non-white characters in the films- well, you can hardly call them characters since they don't have names - at the cinema made me pretty uncomfortable too

This is true of most films done prior to 2010 (filmed prior to 2014-2010, can't remember when I started picking up on a change exactly). I've been noticing a change of sorts for films filmed or created after that. It's subtle but changing. And definitely with television - far more diversified casting since 2014. So, I'm thinking you may find the Amazon series to be different than the film version in regards to diverse casting choices.

There's no reason why they can't be diversely cast -- since Tolkien never states that Hobbits happen to look like short white guys and gals from Britian in the books. That's Hollywood's lack of imagination -- which again, I think is changing. Today, you go into a movie theater and not everyone in the film is white nor are all the good guys white. That wasn't true about ten years back.

Also, the current generation or millenials, have less tolerance for non-diverse casting choices and they make up the bulk of the viewing audience.