Yeah... maybe I would have called it anti-scientism. Far too many believe that everything science currently says is fact and not understanding how the scientific process actually works (including the fact that science needs to continually update what is true because new evidence is uncovered.) Or maybe you could call it anti-empiricism.The word "anti-intellectualism" came about not from people being against intelligence or education. It wasn't (anti-intellectual)ism, it was anti-(intellectualism), where the intellectualism is a synonym for rationalism, the idea that human reason is the chief source of truth and knowledge. As a religious person, I may have a different perspective on that than most of this board, but even setting all that aside, you shouldn't like that idea. Rationalism is in contrast to empiricism, the idea that knowledge comes from sensory experience. Anti-intellectualism, from it's etymology, is not criticism of having or obtaining knowledge, it's criticism of those who act as though their facilities of reason are capable of independently assessing all the truths of reality without outside influence.
That the word has molded instead into being opposed to knowledge or intelligence is a real shame. Exceptionally few people are opposed to knowledge or intelligence, but any reasonable person is against know-it-alls rationalizing their positions. As an intelligent person myself, I can say with confidence that faith in pure intellect is a horrible trap, as intellect is just as capable of rationalizing dumb beliefs as it is of obtaining valid ones.
Maybe that doesn't match so maybe I would call it anti-expertism, which is I see far too much especially in politics. They go in with a belief and deliberately ignore any expert that says otherwise.
But I'm only really doing any of these distinctions because many of the people you could class as 'anti-intellectual' usually ignore outside influence themselves and make up rationalities based purely on belief. They usually are worse and more out of touch from reality than most intellectuals. I.e. anti-intellectual is just identity politics. More being based NOT being something rather than doing something. See also - antifa. They just care about not having fascist. There are a lot of philosophies that can also fit under antifa, even capitalists.
I.e. I personally don't think anti-intellectualism today means either of those definitions you gave any more. I think its been co-opted and lost its meaning. But that may just be my dislike for most -isms and antis-