All things considered, I don't think advanced degrees necessarily correlate with intelligence. It's often just a marker of socioeconomic privilege.

A Carnegie Mellon study found that people with PhDs were more likely than any other educational attainment level to be against the Covid-19 vaccine: https://www.medrxiv.org/content/10.1101/2021.07.20.21260795v... (page 17)

Gallup polls during the Vietnam War found that higher-educated Americans were more likely to be pro-war while the most anti-war group were those with only a grade school education: https://afterthewarproject.org/files/original/3e5e5a47a15203... (page 19 of the PDF, page 38 of the document)