I agree that anti-intellectualism is something I'm concerned with - and that we've always had.
I think part of the problem is that it's too easy for the average person reading the links in their Facebook feed to think that those intellectuals can't make up their minds. It doesn't matter what the topic is, you can find a "study" for it as easily as one against it. I think many people without the time to investigate simply assume nobody really knows the answer, so you might as well have an opinion. And back it up with a "study".
Of course, if you follow the links to the study, you may find it doesn't really say what the journalist's summary says it does. Indeed I've found some that say pretty much the opposite; even if the journalist/blogger is trying to be honest (most are; but it doesn't take many to cause problems), some of them - not all! I have seen some very good reporting - are a journalist/blogger because they didn't want to take science classes in college and they may easily misinterpret the results, or at least their certainty and significance. Or they may simply be pressured by their editors to write something "interesting" (and the headline, an even shorter summary written by yet another person, makes the problem even worse). Or you may find it's not an honest peer-reviewed study at all, but rather a paper by a company with a profit motive or an individual with an agenda that has some mistaken assumptions or is missing pieces of the puzzle. The problem is that almost nobody follows the links to check all that out. Who has the time?
Any article that talks about a study but doesn't have a link or at least enough information for me to find the study, I assume is incorrect. If it's something significant that doesn't match what I've heard before, I follow the link to the study to check it out. But as important as I think it is to do this, I don't have time to investigate everything I might be concerned with. So while much of my information may be as imperfect as others', I don't blame the problem on science or smart people. I think the far bigger problem is with bad science reporting, and dishonest or naive people that are more concerned with making it sound like their assertions are backed by fact than in checking to see that they are, really, backed by fact.