Elitists read a narrow set of books that are considered important, and think they are important because they read these specific books. anti-intellectuals think they are important, because they have read a a narrow set of writings and feel important (Oh, I don't know, maybe the bible)
The funny thing about Republicans and Democrats is that they both accuse the other one of being narrow minded idiots who can't reason. They are both right as far as I am concerned. Listening to a hardcore Republican and a hardcore Democrat argue about issues such as gay rights or abortion is like listening to a couple of five year olds argue about something that neither one really know anything about. Both sides tend to make up statistics, use ugly language, and resort to personal attacks. Now, moderates are ok, they will occasionally listen to an opposing view, and actually let the other person stop talking before they start talking, but loyal party members are basically just trash, they don't really think for themselves at all, their party could start idolizing Hitler, and either party loyalists would smile and agree with their leader the new Father of the motherland.

If you read a lot of response posts, especially about the election, you will see both sides spouting partisan talking points, which generally leads me to believe that people are just vomiting up what they've swallowed entirely undigested. However, the fact is that there is a difference between "the elite" "elitists" "intellectuals" and "liberals" Trying to conflate them all as the same thing is silly. "Elite" just means that you're among the best at what you do, no matter what the field. You can be an elite frog-gigger. However, politically speaking, "elite" just means "just as educated and rich as us, but in the opposite party."