Prefatorily, this is entirely my personal speculation based on examining media in the US versus other countries, and my admittedly minor knowledge of history.

Anti-intellectualism did ramp up in institutionalized education in the 70s, especially with the explicit codification of jock vs nerd, but imho this really started as an unfortunate (and later exploited) knock-on effect of anti-bourgeoisie sentiment after the Great Depression and post-war era. The "All-American" working class man stereotype being contrasted against the intellectual is something that didn't happen in e.g. late 1800s France's anti-aristocratic and anti-bourgeois streak; people viewed themselves as just as capable of matching the intellect of 'elites', rather than turning intellect into a negative attribute.

When we allowed the negative depiction of intellect to permeate entertainment media (in the 50s and especially the 60s), it really set the stage for the current anti-intellectualism we're steeped in. We start teaching kids from a young age that trying to be good at anything artistic or anything knowledge-based is cringe, or nerdy, or something losers do. I've lived in other countries, and you don't see that same effect, even in 'macho'-driven cultures.