I hope you won't lynch me after this one.
There are many ways to differentiate people into two groups. One I can see here, is the difference between the "romantic-reactionaries" and the "modernist-activists". Tolkien surely was of the first class, and I guess many of his admirers are so too. Compare Tolkien to the modernists of his day (eg. the artists, writers, composers, choreographists of the 20's to 50's...) and you can see the difference.
But then he was taken in by the hippie-movement of the 60's, and the rest is "history"... Well the hippies anyhow fought against the then academic and abstractly intellectual art-scene as bourgeois-bluff. Not without a reason I think. Somehow a reactionary became the activist...
I was kind of a hippy as a young guy - and in a sense I am still (I still enjoy Jefferson Airplane, Frank Zappa and even Led Zeppelin) - and love Tolkien. By the same time I tried to make this love of Tolkien coherent with my radical social ideas. That was a tough one, and still is.
But surely I can see Tolkien in a different light now: calling for the best ideas of conservatism: love, trust, companionship, care for others... But still the institutions he kind of sanctified, are dubious to any social activist today: patriarchality, "family-values", social conservatism, sticking to the ways things have been in an idealized mode - not really seeing the suppressive structures behind them etc...
But surely people could be differentiated in regards of liking Tolkien in many other ways also...