> If, instead, that person handed out pamphlets saying that the Pfizer vaccine was experimental "gene therapy" that will result in "infertility," what happens then?

See, e.g., https://www.shouselaw.com/ca/personal-injury/harm-to-reputat...

falsity + malice + harm is a basis for liability in a number of different specific forms, and there very little reason to suspect that a new specific variation of that template would not withstand Constitutional scrutiny.