Others have said it already, but anti-intellectualism at its core is alienation. It’s a lack of trust in academic or professional authorities and substituting that trust for either ones own experiences or complete hallucinations. People will find alternative communities to trust, especially if they can find something that verifies their existing biases.
If you sense something’s wrong with the world, but lack an ability to pinpoint it, you’ll go to whoever seems most immediately relatable to you. Reactionaries like Qanon people ended up in that situation. They no longer trust authorities on information outside of cranks on Facebook.
So the question is how do you get more people to adopt a consensus of reality that’s based on expertise, professional research, investigation, etc? You have to convince more people they’re part of that process and that experts share their interests. America has had that before, but usually in times of conflict against a foreign enemy. The average American used to be really into space travel tech for instance.
There was also a period around the 1890s where the average American was really into electricity as a hobby, like making little circuits or trinkets. It was considered pretty normal back then to have an understanding of how simple circuits like a doorbell worked.