Do Evangelicals hate smart people?
No. But it is such a persistent rumor that it might take something as momentous as another Protestant Reformation to see it die.
Because there are folks out there that do hate smart people. More precisely, there are people of faith who draw a line between "God's Word" and "Man's Opinion." They set up human reason as a force fighting against God's truth. While I think most Christians would agree that human reason is imperfect and limited (as humanists and scientists would probably agree as well) that doesn't make it antithetical to "God's Word." Most Christian traditions acknowledge reason as a gift from God not an enemy of God.