Most likely all the same types of people that feel that anything new to do with Star Wars since the original trilogy has ruined their childhood.
For some people the Lord of the Rings trilogy is their favourite trilogy and the greatest epic of all time (don't care for it myself) and so anything done now will have the same effect for them as the Star Wars fans.
The same will be the case for Thrones stuff. Although since so many people were already turned off by the time and the way Game of Thrones ended (I liked the way it ended) those folks are just eager to dump all over it whether they watch it or not.
So many people just like to hate, crap all over and complain about everything, everywhere all the time.
Even though these people you are talking about do exist, it is very much different with this show.
I loved the SW prequel and sequel trilogy and a big chunk of the Disney SW content (except for Obi-Wan) but this show is just a different animal all together, especially for people like me who know the literature.
The show runners have gone out of their way to create a marketing campaign that is targeted to and marketed by quite specific people, giving it the inevitable woke badge even before any piece of actual content was out.
One of many desasterous examples was the promotional campaign amazon did on their prime youtube channel with several obviously gay and ***** people, none of whom had any knowledge or interest in middle earth and were obviously casted actors (one of them even let that fact slip at one point in the video). These different videos were deleted by prime pretty quickly because they were so counter productive to the marketing campaign.
The actors, writers and producers of this show have all said that Tolkien doesn't really matter because they are doing their own thing, they are "modernizing" Tolkien - meaning putting modern political and social issues into an established and successful literary work.
Why they still call this "The Lord of the Rings" is of course clear, but never adressed by these people. They openly mutilate an existing IP instead of just creating their own one - for obvious reasons, because no one would care or watch this content in the numbers they are when the Tolkien name is added. Nothing I've seen or read about this show is in any way faithful to the actual lore in the books + appendices + further reading material. The show runners constantly say that "it's left open to interpretation" or "Tolkien never wrote about that specifically" which is in 95% of the cases they talk about simply wrong.
People are not haters for pushing back against this. This show is very open and disgustingly proud of it's political and social agenda. They could have done their own thing, written a new phantasy IP completely owned by amazon, but they had to drag Tolkiens name into it. That is why the people are pushing back.