I don't think it's a question of intelligence, but there is a strong anti-intellectual streak on the Republican side. Also a majority of those who take everything on faith vote on that side. I think though, that's a question of gaining votes. Even their hero Bush was an Ivy Leaguer.
There's also no shortage of idiots on the Democratic side (see "Guam might sink"), and there's a large contingent who choose to "believe" science without any critical thought.
They're equally unintelligent.