Not entirely true. In 1905 the US Supreme Court decided Jacobson v Massachusetts, which found that the states have the Constitutional right to establish compulsory vaccination laws in times of health emergencies. In Jacobson, the respondent challenged a law that required everyone in a community or county where there was a smallpox outbreak to be vaccinated. The SCt held that the states' powers to protect public health outweigh the individual right to refuse vaccination. Jacobson has not been significantly challenged and remains good law to this date. So it seems likely that if a state mandated that everyone in the state, or at least everyone in a covid hotspot, be vaccinated, there would be no real legal recourse.