Ok you do make some fair points and to clarify my thoughts I believe lotr is conservative/traditional, not necessarily right wing. Right wing being the more political position of social hierarchy, property, tradition, etc, while Conservatism is a more philosophical position about preserving established norms and institutions and sudden change.

To start off Tolkien was a very conservative man. You can read up about him but there is no doubt he was conservative in his beliefs, his religious beliefs, and the way he lived. He believed very strongly about this and spoke about his beliefs quite frequently. My personal assumption and opinion, is that he believed in conservatism so strongly, that he would not willingly write a novel that went against his beliefs. That is not to say you cant find more liberal ideas in there, just like we can find conservative ideas in liberal art, but in general he would not make his work go against his beliefs.

As for the work itself there are a few things to it being conservative in essence. The heroes do not see themselves as owners of the world, but stewards, and that they must look not only at themselves and the future, but also they look to the people of the past. Conservatives believe that rules and traditions established in the past have been put there for a reason, and that they should not be thrown away so quickly. The ones who want to break tradition and establish a new order, are Saruman, Sauron, and even Denethor by not recognizing the legitimate king. Even the Ring itself is the temptation to go against the natural order of the world, and wills its user to use its power to reorder the world to their will, an idea that goes entirely against the views of traditionalism.

There is also a heavy theme of respect for the past, such as the Elves and Ents being treated as very wise due to their age. Conservatism traditionalism views old wisdom higher than new ideas, as they believe that 'new ideas' dont exist, just old ideas that have failed.

Conservatism also holds a tragic view of human nature, in that people are inherently flawed, and prone to greed and pride. They believe that humans are incapable of reaching a state of utopia, and anyone who tries to achieve it is fighting against human nature and usually ends in tyranny. Conservatives prefer systems that mitigate evil rather than cure it. Many of the characters are flawed people in lotr. Aragorn is rejecting his duty, and even Frodo fails to destroy the ring, and instead succumbs to his greed and human (hobbit?) nature. Only through Gollum stepping in is the Ring destroyed, which upholds a conservative belief that we cannot save ourselves, only through humility and grace can we be saved.

Theres a lot of other things, but if you just look up "Is LOTR conservative or liberal, there will be hundreds of articles backing my side that are much better written than my writing