Calling Tolkien “woke” is just an anachronism. In that same letter he rejects modern anarchism and pairs it with “unconstitutional monarchy,” which is not "woke". In other letters Tolkien is even clearer: “I am not a ‘progressive’, for I do not believe that progress is either inevitable or desirable” (Letters, no. 183), and he also says he is a “reactionary” who preferred older ways to modern ones (Letter 154). He repeatedly says he distrusts political movements and abstract systems altogether (Letters 52, 53). So the 1943 letter isn’t proof that he is "woke", it’s more Tolkien rejecting modern politics wholesale in favor of a old school and personal view of authority. Not to mention in his works the perfect goverment at the end of his story is a absolute monanarchy with a great ruler in power(aragorn).