I just wanted to throw a bit of an extension so this, and keep in mind this is completely of my opinion/observation.
A big drive to what I think is fueling the anti-intellectual movement is a misunderstanding of the scientific research and purpose. Many of the "anti-intellectual" types I've interacted with often cite the same rational for their opinions and it usually falls into a few broad categories:
1) The Egg is Healthy Debate - "First they're healthy, then they're not, then they're healthy again! How can we trust them with this if we can't trust them with eggs!" - It shows lack of understanding that we can change opinion based on new information. Often they want to believe there's this black & white distinction to every issue and can't see the nuances of why something can be both good and bad for you but in different ways.
Somewhat of an additional point to this is people are taking it to mean scientists are often wrong, so maybe they're wrong this time too.
2) Bought & Paid Research - Sugar is the most recent one where lots of people are believing the war on fats was a driven narrative by interested groups. Maybe the food pyramid is a good example; something that was taught extensively but was heavily influenced by Agricultural groups. As an extension to this lots of people think they can ignore science at their leisure because they think everything is a bias from some group sponsoring the research that benefits them.