If you want to fix anti-intellectualism, you first need to fix intellectualism and return it to its roots of dispassionate exploration, commitment to truth over all else and bending processes to find truth rather than bending truth to fit (politicized) processes
Perhaps science was once like this, when it was practiced only by a monied elite at their leisure. But if science, or intellectual life broadly, is important and consequential, it necessarily will not be dispassionate.
Science is a human endeavor, practiced by humans. Scientists aren't Vulcans, and efforts to "fix" them will be as problematic as other social engineering efforts. To get the outcomes desired, one has to change the incentives; changing people doesn't work.