Intelligent people of all political stripes love that movie. The reason is that it is hilarious. "Gentlemen! There's no fighting in the war room!" "But, but you can't let that Russian in here, he'll see the big board!" It's just funny. Every character in that movie is played to perfection, and I still laugh until I almost pee at Sellers' Strangelovian monologue at the end, when he's fighting against his own arm which is displaying a mind of its own with Nazi tendencies. It's priceless.
That's why it's a conservative's movie! It requires intelligence to appreciate. :-)