Consider that many fans watch things they routinely disparage online. For example, many Star Wars fans routinely disparage "Star Wars Episode I: The Phantom Menace," and yet it's still one of the most-watched, highest-grossing movies in the history of cinema.

Also, keep in mind there are people who are really fanatical about LOTR. At the end of the spectrum, some of them enjoy this stuff so much that they regularly attend LOTR conventions dressed up as wizards, knights, hobbits, orcs, etc. Those people will watch the new series even if it's only to criticize all the things it got wrong!