The cause of low vaccine booster uptake mostly isn't the anti-vaxxers, it's the media and political class's decision that Covid was over and it wasn't anything to worry about anymore.
"Get your boosters" and "Covid is over" are contradictory messages, and while all the Nates and Davids and Noahs will say they were vaccine supporters, that message was buried in the general "everyone who still worries about Covid is a bizarre freak" messaging that dominated.