[Rumil]

I think one aspect that you could look at is how LoTR has been applied to various movements and political positions. We know that it is not allegory, and no doubt Tolkien would not have expected some of these, but readers use the story to reinforce their prior positions on many matters.

For example:

A 'Green Party' environmentalist may take to heart the story of the destruction of trees in Fangorn forest or the slag heaps and pollution at the gates of Mordor, contrast these with the Shire and Lothlorien and end up even more committed to their cause.

An anti-communist or anti-fascist may decide that Sauron represents the particular dicatorship that they are opposed to, and use the story as a classic good v evil tale.

An anti-nuclear campaigner might (incorrectly) see The Ring as an allegory of nuclear weapons and nuclear power, that should therefore be cast into the Cracks of Doom.

A royalist might find support for ideas that a monarchy is a good idea, looking at Aragorn reuniting the kingdoms and restoring the line of Elendil.

Etc

Etc

How significant any of these might be is a different question, and probably there's no evidence for direct infuence on the politics/economics/warfare sort of history, but there you go!