>Humiliating him would cut the legs of the movement.
No, it wouldn't, at all. People have been humiliating conspiracy theorists with the facts for decades, and the only result is that conspiracy theory has become mainstream. If all it took was a superior rational argument from an expert to convince people of the error of anti-vaxxers, there would be no anti-vaxxers. Yet even on HN, a forum that should be a nexus of rational thought, they dominate any thread where vaccines are a subject. The "sunlight is the best disinfectant" shit isn't working.
What will happen is exactly what people like RFK want to happen - their message will spread, the "experts" will be reframed and reedited and taken out of context through memes and bad-faith videos and exposes, and people will (as they always do) have sympathy for the "underdog" (the anti-vaxxers) and skepticism towards "experts" and wonder what they must be trying to hide.