Reform Jews, Conservative Jews, Orthodox Jews whose main focus is this world, Orthodox Jews whose main focus is philosophy, Orthodox Jews whose main focus is community, Jews who use bad science to prove Torah, Jews who use bad Torah to prove science, pure atheists, pure believers and so on — all the groups whom Rambam would merely criticize, disagree with fundamentally, call fools or label heretics — all these groups quote Rambam to find support for their view of the world, of G-d and of Judaism.
Perhaps because Rambam is so fundamentally present in Judaism. Perhaps because Rambam was a godol, through whom ruach ha’koidesh spoke — and in G-dliness you can find contradicting, impossible and simply wrong (as far as this world is concerned) things existing in potential or in some higher, untainted form.
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This reminds me of a story about Frierdiker Rebbe riding in a train with a few Russians, each of whom represented a particular school of political thought — a communist, a democrat, a monarchist, an anarchist and so on. They were arguing with each other and then turned to the Rebbe, each asking him to agree with the particular philosophy, citing different passages from Torah and Tanach in support of their ideologies.
The Rebbe told them that Torah is the source of all good in the world. Since the Torah was given at Sinai, its wisdom penetrated the matter of the world, so that Jews can do mitzvos with material objects of the world, uniting them with Hashem. As a “side effect”, even if someone does not actively look in Torah for moral and proper views, just his effort of trying to find an answer to a moral question will attract his mind naturally to the ideas of goodness existing in Torah [even though influences of other sources may confuse and distort his final decision].
As a result, since each of the politicians’ ideologies mixed some good with some evil, the good that was contained in their ideologies could be traced back or at least supported through some statement or idea found in Torah.