Sounds like the author wants to equate the belief in evolution with the right to govern.
If a candidate for President of the United States announced on national television that he believed that the world was flat, and that fantastic sea monsters lurked in the depths near the edge of the world, would you feel he had the requisite knowledge or judgment to be President? For the most part, looking at a politician's belief in science is useful only because it is indicative of his analytical abilities, and someone who believes in sea monsters or creationism probably also doesn't have the requisite analytical abilities to manage bureaucracy, defeat terrorism or keep social security solvent.
But belief in evolution may be useful for policy as well. Suppose that there's an epidemic, and the President refuses to take certain preventative measures because he doesn't believe the pathogen can evolve. In that case, hopefully unlikely, people could actually die because of a failure to accept modern science.