[Zigûr]

Something that might be worth considering is that Saruman and Denethor are both "politicians" to a much greater extent than other leaders in The Lord of the Rings. Saruman is full of hollow political spin: "There need not be, there would not be, any real change in our designs, only in our means." And his plan to manipulate Sauron I think conforms to this as well.

Professor Tolkien observes that Denethor was "tainted with mere politics... It had become for him a prime motive to preserve the polity of Gondor, as it was, against another potentate", hating Sauron not because he was an evil being who, morally speaking, had to be opposed, but simply because he threatened Gondor's statehood. By contrast he remarks that "the Elves destroyed their own polity in pursuit of a 'humane' duty" by allowing the Three to fail. (Letter 241)

I think Saruman and Denethor are both leaders who had lost perspective and were not interested in the 'big picture'. Was this a symptom of Sauron's influence? We know that he believed "Eru had simply abandoned Eä, or at any rate Arda, and would not concern himself with it any more" (Morgoth's Ring), so maybe he himself had lost perspective in the same way. All three of them, I think, treated many other people like tools rather than individuals with inherent value, which might explain why they were keen to accuse others of doing the same, especially Gandalf who was the mutual opponent in many respects of all of them, even Denethor from an ideological perspective. Observe that the Mouth of Sauron, too, another of the 'political' characters (along with Smaug in The Hobbit, I might argue) also accuses Gandalf of manipulation while he himself is toying with the Captains of the West. It may have been a limitation of all of them that, incapable of true altruism, they were equally incapable of recognising it in others.

But I think it might come down to an idea which is borne out in a study of how Sauron's early utopianism was perverted so easily into tyranny and evil: because it exacerbated one's tendency to view other people as either tools or obstacles (thus forgetting that the designs were originally meant to be in the interests of everyone, which is to say the people about whom they not longer cared beyond their instrumentation). Gandalf was an obstacle, but an obstacle of sufficient power that they viewed him as being of the same nature as they were. I daresay Denethor and Saruman, who allegedly did encounter each other in the Stones, also harboured similar feelings about each other.