The Intelligent Design/creationism crew would have us believe their theories have influenced science, but where their behavior has really had influence would seem to be politics. Take the Gish Gallop, a favorite technique of creationist debater Duane Gish. Gish would rattle off as many lies about evolution and scientists as conceivable in a very short span of time to overwhelm his opponent's ability to refute them, since refuting a lie takes far more time than uttering it does. Thus, many of the lies would go uncorrected, and Gish would leave the debate audience under the impression that, even if Gish didn't win the debate per se, there was enough there to cause some doubt as to the validity of evolution.
Well, the Gish Gallop has become the Palin Prance. Further, Palin has, as Ann Coulter did before her, taken a page out of the ID playbook and refused to even acknowledge the corrections of her lies even exist. Coulter wrote an execrable chapter on evolution in her book "Godless", after being coached by prominent ID proponents, which was described by one biologist as "wall to wall error". Many bloggers and writers took the time to, point by point, refute Coulter's work. Yet Coulter to this day claims no one has ever criticized the science in her book. Likewise, Palin keeps repeating the same lies over and over again, completely ignoring the refutations that exist. And to no one's surprise, Palin is parroting the "teach the controversy" ID chant.
Those economic Republicans who dismiss the loony religious wing of the party, and it's religion-related errors in politics (resistance to abortion, stem cell research, etc.) as immaterial to the big picture make a substantial mistake. Such lazy thinking, and refusal to honestly engage one's intellectual opponents, will seep into every issue. Palin is Exhibit A of this problem. There is no corralling sloppy thinking, and it seems every time someone gets near the ID crowd, they get infected with it.