Amid a brazen, state-sanctioned disinformation campaign against a ballot measure to restore abortion rights in Florida — including visits to voters’ homes by Republican Gov. Ron DeSantis’ election goon squad — doctors say the state’s ban is putting their patients’ lives at risk, forcing them to confront unfathomably dark medical scenarios, and some are warning they may be forced to leave the state if the measure fails this November.

The Planned Parenthood Health Center in Miami, Florida, has remained open, but since May 1, there has been a big sign in the lobby informing patients that,...